Yes, if you push me like that I'll say it: it's incompetently overdone.
When your goal is to "reduce clutter" then 2 layers would be the minimum. You make another 4(?) folders in my home-directory and call that reducing clutter?
And when I delete an app then I have to look in all of them?
That is just utterly backwards for no conceivable reason.
Due to the semantics you now suddenly need a cronjob or similar abomination that traverses all home-directories and picks out stuff ("MUST" be blown away). This will by definition be fragile and have funny corner-cases in the first few iterations. Also what happens when ".run" is not blown away, like on a system that does't implement this nonsense?
The definitions are blurry and complex, many apps will get them wrong (.local vs .config etc.).
Unix already has a location for temp files. It's called /tmp.
And what the heck is going in .local anyways? When the user saves a file then he pretty surely doesn't want it buried under some dot-directory.