Mostly agreed with Forbin, except I've been toying with the idea about how to use warp and impulse engines at this speed, in addition to shields and deflectors. I doubt the engagement would really be as simple as "hit him before he hits you." Your Klingon attacker might take several hits and chose to disengage, but if he's really pissed off you're going to still be fighting him for another ten minutes before one of you can claim victory.
I figure out it's like swords and arrows. (Bear with me on this one) at long range, you can shoot torpedoes at the other guy (arrows) or close to short range and hammer him with phasers (swords). Sword duels are only quick and brutal when they don't involve armor or some protection; if you have a short sword in one hand and a shield in the other, it might take you a minute to get past that shield and get some good happy stabbing done. So, exactly what tactic you use depends on what the other guy is equipped with. Someone with, say, deflector screens tied into his warp drive is going to be able to repel your torpedoes almost indefinitely, so you're going to have to get in close with phasers and either knock out his deflectors or force him to transfer that power to his engines just to get away from you. At that point, you either finish him off with the phasers, or you let him get some distance and hit him with torpedoes (or both). If he's got a lot of heavy armor, you don't have a choice: a phaser or torpedo strike will have to hit him in a sensitive spot to do any damage.
Starship combat would probably degenerate into knife fight ranges more often than you'd expect, as ships get closer and closer in an attempt to thwart each other's defenses and make more of their own shots hit. Jumping back out to a distance -- if the other guy gives you time -- can give you a chance to catch your breath and regroup before pressing the attack again, but the nature of heavy shielding and deflectors means it's still more likely to be a sword fight than a sniper duel.
One of the reasons I figure why nobody ties their deflector dish directly to the power line of their warp core is if there is any feedback due to overloading the shield, that feedback might take out the warp core and the ship itself. That's probably why all shields are on it's own large capacitor. Should the shield go down, or get overloaded, it won't take out the ship.
I do agree with your analogy in the general sense, the details and reasoning of why you do the things you do is where I would differ.
Fighting at Super long Range (> 100 km)
- Harder for enemy to hit you in general
- A small amount of movement in any direction that is perpendicular to your enemy can cause them to miss energy weapon shots.
- Gives you more time to shoot down Torpedoes or other slow moving projectiles
- More time to recover from damage and solve any crisis due to damage
- Easy to protect the weak side of your shields just by rotating yourself so the enemy doesn't have a clear shot at the gap in your shields.
- Easy for the side with a worse situation to run away or prolong the fight.
- Incredibly hard to target a specific subsystem if the enemy just chooses to rotate their vessel so that the weak side of the shields isn't exposed.
- Incredibly easy to miss if the enemy pilot knows how to dodge.
- The fight becomes a war of attrition, any side with not enough resources will lose.
- Both sides are vulnerable to torpedoes with large explosive area should they choose to employ such weapons. Modern nukes have huge area of effect, if any side chooses to field such weapon, both sides may be screwed.
So the advantages of fighting at close range (<= 10 km):
- Easy to hit subsystems or weak side of shields.
- Easy to position yourself around the opponent, especially if you killed the weapon banks on one side, all you have to do is stay in their blind spot.
- Gives the weaker side less time to recover
- Harder to miss in general
- Discourages both sides from using wide area of effect explosives without fear of taking damage themselves.
- You can tractor the weakened foe to make it harder to escape.
- Once you knock down their shields on one side, you can easily beam over assault parties to capture their ship.
- Easy to be hit in your own subsystems or weak side of shields.
- Easy to for the enemy to position themselves around you, especially if your weapon banks on one side are dead, all they have to do is stay in your blind spot.
- Harder to hide the weak sides of any shields since travel distance to face a weak side of any shields is significantly shorter.
- If the enemy looks weakened but is still strong enough that they can cripple your FTL engines and STL engines, they can commit double suicide by overloading their power source and take you out with them should they be desperate enough.
Alot of times I doubt any fight in the Star Trek Universe would stay at long ranges. There are just too many good reasons to get close and take risks.