Have you heard of the cancelled Penn and Teller video game Desert Bus?
It takes 8 hours to beat, requires your constant attention, and can't be paused. I'd say that still falls into the "possible to beat" but you could keep pushing the limits further.
What if there were 10 levels like that but you can pause between levels? Still technically possible. What about 1000 levels? That requires almost a year of active playtime, but there are pro players with that many hours in their game. Where's the limit? 10K? 50K? 500K? I don't know.
Of course, this is all just a random thought experience on what it means for a game to be possible to beat. I don't think there's an empirical way to define the boundary between possible and impossible, but we could also just restrict it to "games that have been beaten at least once by someone and are provably beatable".
Ultimately I do agree with you though. There are just too many games out there for this to be possible anyway.