Yeah you would want it to be a little smarter than I described, but not too smart. Web browsers would remember their tabs and windows, office programs would autosave and autoload temp files, etc.

I imagine there's a hundred tiny problems which make it infeasible, and it would require API changes, but damn would it be nice.

Mostly it would require all of the apps you use to release new versions that support checkpointing their internal state when asked to by the OS.

There's basically no way for the OS to do that for them, they'd each have to implement it themselves in a manner specific to the application.