I'll  say it now, rushing in this game is extremely effective.
Even the earliest attack consiting of 6 LRMs and a capital ship is absolutely devastating against someone who hasn't prepared the appropriate counter which also requires the construction of 2 military research bases and a military focus.

Someone who builds trade centers and broadcast centers, even if they do max out their fleet cap, is typically dead.

How do we solve this?
By making it difficult to rush central planets in the early game, and making it easier to attack them in the late game.

Enter culture.
Culture bonuses ought to kick in immediately, and grow with research, instead of initially requiring research. They should also be -much- more substantial, perhaps twice or three times the effectiveness they are now.

Well, you say, wouldn't this be a complete pain later in the game when the defender is three times tougher in his home territory?
The solution is to tie cultural bonuses to allegiance. Planets farther away from the capital are naturally less loyal, allowing outlying planets of empire to be more vulnerable.
Capital ships should supply more culture drain per capital ship, making capital ships -the- perfect tool for assaulting deep into enemy territory.

On that note, wouldn't people just put the capital on their borders? That solution is easy- destruction of a capital should have an immediate effect on allegiance all over the empire, and make moving the capital take longer (but not neccessarily more expensive)

This allows a perfectly dynamic game- does one take border planets and absorb resources, slowly chipping away at the empire, or strike at the heavily guarded broadcasting centers and home planet, deep in the empire in unfriendly territory with a fleet of defenders hounding your back?

This would require a great deal of balance, and  perhaps may be more appropriate for an expansion pack.
Let's see!