Aliens do not cheat with resources, so if you let them harvest resources for a long time they will spawn hundreds of ships, and yeah in that even finishing the game is a chore. You can destroy their bases earlier to avoid that. Generally speaking if you go past the mid 40s without having engaged the aliens seriously you are in for a huge war of attrition.
Alien stations you can fight against them and are not so scary as bases are, though they are not necessarily easy, it will depend on the size and composition of your fleet. But bases will melt down bombarding ships in my experience. I know they've been rebalanced but I tested it last game and it was a total failure with a regular combat fleet just the same.
To destroy bases nowadays there's basically three ways:
- Bombard with insanely armoured ships, I am talking about 500+ front armour, people who do it use dedicated bombard ships, but I have never done it so I can't say more.
- Use a leader with the "Destroy Space Asset" mission, but this means having a leader wasting lots of time travelling around, this doesn't require lengthy repairs of the Marine Modules.
- Use many space marines, alien bases have about 200 marine power (you can see it when you select them) just bring about 20 more than they have and you will succeed most of the time. Of course this forces you to repair after each assault but you can do it at an space base you can construct with another ship. This is my preferred method since you can make very cheap ESCORT/FRIGATES Assault ships.
If alien administration spawns in an isolated backwater country you can let it be for a time, just make sure you are at war with it so it doesn't have "freedom of the seas", in that case it doesn't do much other than conquer some other neighbouring backwater countries.... I find a lot more problematic when the aliens land many armies, these can be enough to cross oceans from the get go and maybe finish off China or the USA in a moment. This can make stopping it later very difficult, though Alien administration eventually has very serious problems with unrest.
Anyway the late game is one of the weak points of this game.