And if this was the late 1930s, that would mean something.
And if this was 1920s?
Because spaceships... can't... fly?
Because space battleship and space fighter are in the same medium.
The air power dominated the naval warfare because aircrafts move in air, and warships move in water. There is difference in mobility that couldn't be avoided.
With the spaceships - there is no reason why battleship must have less acceleration than fighter.
I don't know what they told you over there, but it's been known in these parts that in the event of a shooting war with the Soviet Union, the lifespan of a U.S. carrier group anywhere along the Russian coast would be anywhere between 10 and 30 minutes.
Sigh.
Just... read the history. In 1982, the "Midway" actively operated near USSR coastlines for FOUR DAYS - and our navy doesn't even knew that it was here.
Please, read the history first, than threw some nonsence. You knew nothing about carrier tactics of the cold war.
Meanwhile, the Russian carriers -- I'm sorry "Aviation cruisers" -- were never designed to be a counterpart to American carriers. They're power projection systems, just like the carriers are. The Soviets had NO plans to take on the U.S. in carrier-to-carrier plans because they knew they couldn't build carriers powerful enough to make the contest interesting. They DID build the most advanced submarine force the world has ever seen, though, and that would also have sucked to deal with, but I digress...
...And you knew nothing about USSR carriers, obviously.
Thei main goal was to provide fighter support for maritime reconnaisance and strike aircrafts far from coastlines, to disrupt the enemy aerial reconnasiance and to support anti-submarine operations.
Then weren't supposed to take on the US carriers, yes. They were supposed to provide cover & reconnaisance for USSR missile-carrying aircrafts and submarines, which were supposed to attack the US carriers.
Please, stop talking about things you knew nothing about.
Because every fighter squadron on the west coast is just going to sit there and eat pizza while that carrier group carefully walks up to strike range of Seattle and starts launching attack planes before thinking "Gee, we'd better get up there and do something about it."
And you assume that carriers would just sail in parade formation, signaling "we are carriers!" to everyone around?
Read this first:
http://www.navweaps.com/index_tech/tech-031.htm
Then we could discuss.
The California, Orgen, Nevada and Washnington ANG all by themselves can match those numbers AND have greater logistical support, not to mention a larger number of ground-based anti-aircraft missiles with far greater range than the carrier's sea-based weapons. And this before you factor in the ACTUAL AIR FORCE stationed along with them. In the end, your three carriers and 200 planes are up against 1000 fighter craft and ten times their weight in firepower. This is not a smart thing for anyone to do.
One small problem. You land-based planes have no clue, where the carriers are.

If they send reconnaisance aircrafts, they would be shot down by carrier fighters. If they send fighters to cover them, the land-based fighters, operating on the long distance from their base, would inevitably lose to carrier-based aircrafts, which have their base much close and could operate with much greater ordnance payload (while your poor land-based fighter would carry mostly the drop tanks).
So while your enormous airforce seems powerfull, in fact, it's the essentially blind, and tied to the place Goliath, trying to hit David.
Starship combat has similar logic. Weapon systems can be stored in larger numbers in fixed installations than they can on starships. It's even worse when you consider that the ranges of these weapons means that ANY installation on the planet can be brought to bear against ANY target within its line of sight; attacking starships can fall back out of range, but there's nothing much they can do to avoid detection except cloak themselves, and Federation worlds are protected by those pesky tachyon detection grids whose rules of engagement appear to be "shoot on sight."
Again: there is NO range for kinetic projectiles, and the rocks are ALWAYS cheaper than torpedoes.
This is exactly the reason, why in Cold War USA quickly gave up on the ideas of land-based missile defense for cities. They weren't cost-effective. The anti-missile cost MORE than ICBM or SLBM that she was supposed to shot down (and then the multiple warheads came, and situation became even more dire). The enemy could awlays concentrate the ICBM and SLBM strikes, while the ABM's could not be concentrated - I.e. enemy could always just saturate the defenses. And, to be effective, the ABM must be absolutely effective, because just ONE missed warhead means the destruction of the protected "soft" targets. The ABM's were fighting the lose battle; to win, they need to intercept EVERY warhead per given object, while the attacker need only the single warhead to not be intercepted to win.
Just imagine the shooting contest, with said rules:
* To win, you need to hit the center of EVERY target, If you missed one center, you lose.
* Your opponent, to win need to hit ANY target at all, not even in center.
How good is your chances to win? Even if you are the best shooter in the world with laser-scope, and your opponent is newbe with matchlock pistol, you chances is just statistically worse. Any mistake from your side, any distraction - and you lose.
This is the fundamental rule of mass destruction warfare, guys.

They work in space, too.

There is no point in shooting down the projectiles - the opponent could always bring more.