This isn't really true. At least on the steam deck. Of the 156 games I have in my library, 52 of the are "great on deck". Id say twenty of the other ones work great anyways.

I don't play multiplayer games, but the one I do have are in the works great category. The vast majority are single player games. (Just checked, i have 15 games that not compatible at all)

Definitely double check your games before making the switch.