ASGI is disgusting. It's WSGI (not very good in the first place) with asyncio tacked on (even worse!).
I have not had a chance to play with ASGI yet. I'm not a fan of async as a paradigm, but it has a small number of use cases where it excels. I think it will always be problematic when you need heavy database access (like in most django apps), but where it does fit it can be a very handy tool.
About the only nitpick I can think of is that dealing with large streams of data (say a user-agent uploading a big file) without either the web server / or the WSGI side of things reading the whole thing into memory or buffering it on disk can be a pain.