Actually, carriers would NOT necessarily be viable. Given even current electronics capabilities, there are very few things a fighter could do that a missile couldn't do almost as well. Plus the fact that you could build missiles smaller, faster, and cheaper - no pilot, no life support, no fuel to get back, etc.
another thing i want to bring up is that no combat ships benefit by increasing distance... if it is hard to land hits your fleet is going to close with thier fleet...
This is not necessarily true. It assumes the accuracy of both sides improves equally with decreasing range. If that is not true, one side would have a decisive interest in holding the range open. Sure, you may lose 50% of your accuracy at 2 light seconds, but if your opponent loses 75% at that range, you'll do everything possible to keep your distance. As long as you dont' run out of amunition, you'll win the battle because you're landing twice as many hits.
And, if you'll permit me to be that "dumbo" - even in the era of aircraft carriers (WW2), range mattered. Even with fire control radar, accuracy improved with decreasing distance - but if you could land even a couple hits before the other guy could get in range, you started with a massive advantage. The Yamato was designed for this specific purpose. It could lob reasonably accurate shells so far that it couldn't spot it's own fire, they had to use a plane to see the target. And then, of course, the Americans killed it with an even longer range weapon system - torpedo bombers. Today, of course, we would use a cruise missile - because the missile can do the same thing as the bomber did 60 years ago, but it can do it faster, more accurately, and with no risk of life to the side making the decision.