I think people may ask "why in stdlib?".

My reasons are:
 - We are adding new asyncio APIs in 3.11 such as TaskGroup, so I think it is a good time to add another one, as long as it does not break existing stuffs.
 - I believe that long-running task sets are equally representative use-case for real-world asyncio applications, particularly for servers.  Why not to have intrinsic support for them?
 - PersistentTaskGroup is going to be universally adopted throughout my 70+K LoC asyncio codebase, for instance, in every aiohttp.Application context, plugin contexts and modules, etc.

Of course, the name "PersistentTaskGroup" may look quite long, and I'm completely open with alternative suggestions.  I also welcome suggestions on changes to its functional semantics based on your experience and knowledge.