I'm not an area expert, but common issues raised over the years:
- HTTP/2 as implemented by browsers requires HTTPS, and some people don't like HTTPS.
- HTTP/2 was "designed by a committee" and has: a lot of features and complexity; most of those features were never implemented by most of the servers/clients; most of those advanced features that were implemented were very naive "checkbox implementations" and/or buggy [0]; some were implemented and then turned out to be more harmful than useful, and got dropped (HTTP/2 push in browsers [1]) etc.
- HTTP/2 as implemented by browsers requires HTTPS, and some people don't like HTTPS.
- HTTP/2 was "designed by a committee" and has: a lot of features and complexity; most of those features were never implemented by most of the servers/clients; most of those advanced features that were implemented were very naive "checkbox implementations" and/or buggy [0]; some were implemented and then turned out to be more harmful than useful, and got dropped (HTTP/2 push in browsers [1]) etc.
[0] https://github.com/andydavies/http2-prioritization-issues
[1] https://developer.chrome.com/blog/removing-push