That's not really true though in reality. Explorer does do stuff when you aren't focused on it. If you are transferring files it still copies them over even if you start surfing the web. If you are playing a game windowed and alt-tab out it still runs.
I'm not saying that nothing actually happens, I'm saying that what needs to happen is more restricted than you think. Hence, why unlimited background processing may not be the right answer.
Especially true for explorer. The pop-up for transfers is a specific subset of functionality that benefits from running in the background. That's something that can possibly be tackled in a limited way, just like how we have periodic tile updates, background downloads and uploads, etc. Of course, Windows Phone doesn't currently have a reason to have large file transfer, but in a hypothetical scenario that it did, it could be a background task that will be restricted in IO / processing, and can be paused / resumed from a notification centre.
Singleplayer games could be frozen in the background with no repercussions; indeed, in many cases I wish they were. Point taken for multiplayer, though the performance hit there can be pretty significant and I'm not sure that will always make sense. Especially on portable devices, I'd like to see games move to a place where they can be put in the background, resort to a low-resource mode, then resume fairly quickly.