It’s basically what the Steam Deck does, and for a gaming device it makes a lot of sense. The vast majority of games will probably be installed to the user’s home folder anyhow…
It might be that some games require additional libraries that don’t come with the immutable base OS, but you can always install them in a custom folder (like, the game’s install dir), or just install Steam and use the Steam Runtime for everything.
And, as you said, a lot of open source tools and games (DosBox for instance) are available as Flatpaks too.