Even so, a starship definitely has all the bases covered. The Navigator (Chekov in this case) has a direct feed from the short range and gravitic sensors that can get him a pretty general depiction of what's happening around the ship; any details they need can be extracted from the more detailed scans of the science officer.
Which has what to do with the ship having a windshield?
To retrace the discussion (since you have obviously gotten lost):
You: Windows make no sense. Computer monitors would be better at displaying information.
Me: Fighter planes have windows
You: Fighter planes have lots of instruments and sensors though
Me: So do starships
You: Which has what to do with the ship having windows?
Me (answer): Airplanes have windows because pilots insist on being able to see what is outside of their aircraft with their own eyes. Space craft have windows for the same reason. Even flying on instrumentation only, there is still a need to sometimes read visual cues from other ships; this is canonically established in "The First Duty," and is generally implied by the presence of color coded running lights on Federation starships. Running lights are VISUAL navigation cues used by other ships when flying in formation or maneuvering near each other; an instrumentation-only system would use radar beacons and other systems that would have very few visual traces.
The helmsman has enough to do just maneuvering a ship without having to track targets and fire on them in addition to that. It's a ship, not a fighter.
Which leads me to recall that the first astronauts were originally test pilots, not sailors, and this is likely to remain true even into the 23rd century. Obviously, starships are much larger and more sophisticated, but the need to have the man at flight control still be in the loop for the release of weapons seems to be a distinctly aircraft/astronaut tradition (satellite deployment is handled the same way on modern space craft).
Anyway, since it is implied that the helmsman is only coordinating with the gunners in the phaser control room anyway, it's really a pilot/bombardier or pilot/WSO combination. This works well enough in conventional aircraft where the pilot has to keep total control of his aircraft every possible second; in a starship where the computer does most of the work and the rest of the bridge officers handle the rest, the helmsman would find this rather simple.
No, a ship is not a fighter. A fighter has a canopy (and not just a windshield) in order to give the pilot good all-around vision during close-in dogfights.
Largely irrelevant, since even non-fighter aircraft still have windshields. Even the B-2 Spirit, which in night operations flies
entirely on instrumentation, has simple glass instead of a camera-monitor system.
So the point stands: the bridge has a window because people on the bridge need to see what's outside the ship. For the same reason
any pilot would, no matter what they're flying.
Or it wouldn't have done them any good unless the Reliant happened to be right in front of them and the bow wasn't blocking the view.
Except when Reliant WAS in front of them, targeting the ship visually wouldn't have been a problem since they could physically see the ship hanging there in the middle of the gas cloud without the staticy camera view.
A partially obstructed clear view is preferable to a grainy TV image any day.
Actually it showed a 2-D representation of 3-D space. Kind of like radar screens.
I remember they originally had little bars underneath each icon to represent elevation from the ship's ecliptic, but this was dropped for simplicity later on.
Which doesn't invalidate having a viewscreen instead of a window. If anything the fact that it could do those things shows an advantage to having a viewscreen.
Hence my second point: in Trek, starships COULD do this, but very seldom DO. It makes more sense to redesign the viewscreen to turn this into a secondary function instead of a primary, with the viewscreen's basic functionality now remaining its primary (i.e. "what we use it for most") function.
The thing is, it has been used as a tactical display before.
And it was in the movie, and it will be again in the future. But since MOST of the time it will not be used as a tactical display, its basic functioning is as a view to space outside the ship, and therefore a transparent surface is the most efficient way of achieving this. Since said transparent surface can be made to project pretty much any image the Captain wants it to--including but not limited to tactical displays and engine schematics or whatever else is going on today--there is no loss of functionality while the crew GAINS the ability to see outside of the ship without having to rely on sensor devices.
It's also been used to zoom in on something they want to see, or to change angles to look someplace that isn't right in front of the ship. It's not exactly unusual to want a front and center default setting to the viewscreen either, which is probably a view from the very front of the ship instead of a view from the front of the bridge module (since we've never seen the bow of the ship in the standard view).
And the specific reason a HUD cannot do this is...?
Come to think of it, they did a few things with the viewscreen that previous trek shows have NEVER done. Most glaringly, showing the Captain's vital signs on an away mission, displaying threat tracking data on incoming torpedoes relative to the ship's position, warning icons and indicators that convey in a single word what would normally take a science officer fifteen seconds to spell out... if you ask me, the ability to pan the viewscreen to a "Oh! Look at that colorful image of a torpedo racing towards us!" shot is a bit overrated. They could do it if they needed to, but what they've done INSTEAD is a lot more practical.
What's funny is that I already argued this point. Not only did I complain about starships being treated like sailing ships of old, trading broadsides, or being treated like WWI dogfighters, but I pointed out that at close range that window would be just as useless as it would be at long range due to the limited field of view.
Which again leads me to the question "Then why do airplanes have windows?" Which is similar to the question "Why do (real) space ships have windows?" Bear in mind that real space craft seldom engage in combat, so that probably isn't a very workable theory.
Seems to me that not only have we seen the helmsman use the viewscreen before, but that actually makes the most sense because he or she could see things much better that way instead of having to rely on a tiny monitor on their console.
Depends on what the monitor is showing him. Likewise, even Spock got most of his pertinent information while staring through a three-inch eyepiece mounted on the science console, alot more information than he could have gotten from the viewscreen.
Have you noticed that the wheelhouse for those big cargo ships tend to be at the very back of the ship? That's so they can look out over the ship to see what its condition is as much as it is to maneuver the thing.
Keyword: LOOK OUT. They're not piloting the ship with closed circuit video cameras, are they?
Why do you think that is?

If a large ship didn't have those docking wings then they'd pretty much have to use some sort of camera system.
Then why do they still build large ships with those docking wings?
Oh, wait. You answered my question already:
so far it's just been easier and made more sense to have some helm controls in the bridge wings.
Because helmsmen--like pilots--often need to navigate a ship with their eyes as well as with instrumentation. If the instruments cannot show them what they need to see, then they need to be able to physically look outside the ship to see what's going on.
Hence the need for a window on the bridge.
That isn't the case even with modern weapons.
What modern weapon do we have that is reliable against maneuvering starships in interplanetary space at distances greater than 100km? Hell, even anti-air weapons seldom have that kind of range, and they're shooting at targets that are far less powerful and less maneuverable than starships.
The closest thing we have is the RIM-163 ASAT missile. These can hit targets in low orbit, altitudes of around 400km. They require coordination and pre-launch guidance from a dozen different tracking stations and a ridiculously high degree of precision to make the intercept. After 200 years of development, you would probably be able to do the same job with more powerful weapons and a more compact sensor suite, but the RANGE probably wouldn't increase all that much; maybe 800km at the outset, assuming we're just talking about torpedoes. It gets even more complicated when talking about directed energy weapons (phasers et al) whose ranges could well be much shorter.
Not really. If anything, since it would be a lot harder to hide in space, you tend to want to be the one who not only sees the other one first, but the one who can reach out and touch the other one the furthest and fastest.
Any particular reason this does not hold for air combat, where the exact same conditions exist?
Answer: because FIRING first does not guarantee HITTING first, nor does it by any means guarantee victory. Even air combat at BVR ranges more often than not devolves into turning fights at relatively close range because long and medium-range missiles do not always do the job in the first salvo, or even in the second, and because for every technique some elite pilot comes up with to keep the enemy at long range, some slack-jawed yokel flying out of a plywood airfield comes up with a technique for sneaking in closer, where longer-range weapons won't be as effective.
It effectively boils down to what tacticians have known for centuries: no matter what the medium, battles are almost never fought at the MAXIMUM range of the available weapons. This is why all modern militaries still teach close combat to their soldiers: sure, your M4 Carbine has an effective range of around 200 meters, but in most situations it's going to be used against targets 20 to 50 meters away. If you run out of ammo, if your gun jams, if some crazy Spetznaz runs around the corner and hits you in the face with a shovel... what do you do, lecture him about the logic of battlefield tactics?
It depends on who they are fighting and the circumstances of the engagement. There are plenty of instances of when the pilots of modern aircraft never even see their enemy with their own eyes when they shoot them down.
Correction: there are plenty of SCENARIOS where this happens. In actual practice--that is, in the battlefields over Vietnam, Cambodia, Israel, Afghanistan (both times), Iraq, Iran, Argentina, even in some wargame exercises, this is the exception and not the rule.