Personally, I'd like to see something like Stargate captured in a modern war game - alien invasion, fought here and now with present tactics.
When we get alien invasion games, they're either set far enough into the future for it to feel disconnected from us (Halo) or set after the invasion has been fought and lost (Resistance).
The interesting part, for me, is the transition - How we change in response to first contact.
Going back to my example of Stargate, human society and capacity changes over the course of the show - from a modern-day society to a basic starfaring one, and I think that a game could capture that same sense very well.