That would be pretty disappointing if they can't handle normal processes too. It's easy to end up with a bunch of processes that are using small amounts of CPU but aren't dedicated background tasks.

Even just looking at a browser, I might have half a dozen generic tab processes open, each using a small amount of CPU. But then I navigate one to a game, and I want that particular tab to get near-exclusive access to the big core while the others use only the little cores.