I suppose my negative experiences with async fall under #3, that it is hard to maintain two APIs.
One of the most memorable "real software engineering" bugs of my career involved async Python. I was maintaining a FastAPI server which was consistently leaking file descriptors when making any outgoing HTTP requests due to failing to close the socket. This manifested in a few ways: once the server ran out of available file descriptors, it degraded to a bizarre world where it would accept new HTTP requests but then refuse to transmit any information, which was also exciting due to increasing the difficulty of remotely debugging this. Occasionally the server would run out of memory before running out of file descriptors on the OS, which was a fun red herring that resulted in at least one premature "I fixed the problem!" RAM bump.
The exact culprit was never found - I spent a full week debugging it, and concluded that the problem had to do with someone on the library/framework/system stack of FastAPI/aiohttp/asyncio having expectations about someone else in the stack closing the socket after picking up the async context, but that never actually occurring. It was impenetrable to me due to the constant context switching between the libraries and frameworks, such that I could not keep the thread of who (above my application layer) should have been closing it.
My solution was to monkey patch the native python socket class and add a FastAPI middleware layer so that anytime an outgoing socket opened, I'd add it to a map of sockets by incoming request ID. Then when the incoming request concluded I'd lookup sockets in the map and close them manually.
It worked, the servers were stable, and the only follow-up request was to please delete the annoying "Socket with file descriptor manually closed" message from the logs, because they were cluttering things up. And thus, another brick in the wall of my opinion that I do not prefer Python for reliable, high-performance HTTP servers.