Some games (I'm thinking FFXIV) will run on a lower framerate (15fps) while minimized or, in that game's case, if the player is idle for an X amount of time, that's a pretty decent compromise.

But yeah, games don't need to render any frames while minimized. I do feel like this should be the operating system's responsibility as well, but then, a lot of games still have the graphics rendering and other parts of the game linked tightly together.