Well I kind of alluded to it, but both of the games lack any clear solutions other than "play the game kill the bad guy".

Which, to be fair, is probably the reason BioShock 1 at least got so popular. I would say this point is much more important to BioShock 1 than any commentary about Ayn Rand, or any commentary about how worker's movements can get subverted by selfish actors like Atlas. It takes the usual tropes about videogames and turns them into a commentary on how easily our assumptions and expectations can deceive us. Players do what the game tells them to, they progress the way the game allows them to, without ever questioning whether that is the morally correct thing to do. I would say that's a pretty reasonable thing to do considering the money these games cost, but BioShock at least shines a light on that and makes the player think about it.

There are plenty of other examples of games that DO engage with political ideologies, and use games as a mechanism to think about then. The most famous one is probably Monopoly, which was stolen from the original creator who called it "the landlords game" to show how capitalism eventually leads to one rich person and a bunch of broke people.

If you want a videogame, Disco Elysium is a fabulous, recent, and well-reviewed example. Personally it's a bit dense for me to play for too long (sometimes it feels more like reading a textbook than playing a game).

I don't think BioShock 1 or Infinite are terrible or that they shouldn't have delved into politics at all. I think that they are overrated in part because they get credit for political commentary that ends up being pretty superficial. I think they could have executed the ideas better.

Fitzroy for example: either give us a better reason to fight her or don't make us do it. Maybe she gets killed by Comstock and leaves a power vacuum, with the chaos of rebel leaders trying to promote solidarity, fight for their own power, hold off or even negotiate peace with Comstock. Or maybe someone like Lady Comstock or Fink could be a source of division within Comstock's ranks. Or maybe Fitzroy gets convinced that she needs to kill Elizabeth because she's some dimensional McGuffin protecting Comstock. Maybe get rid of the rebellion entirely and have another country attack Colombia. They already ceded from the US- surely Uncle Sam isn't cool with losing this technological marvel, nor having this independent state potentially floating above US territories. It's been a while since I replayed it but I remember the Boxer Rebellion being a key piece of the story: maybe some fallout from that cones to Colombia.