Yes - used rustls on a new project rather than the openssl wrapper which we used before. The experience has been pretty good. The problems of shared library version inconsistency have gone. No noticeable downsides.
Sure, as long as you commit to releasing an updated version if a vulnerability is ever found in your version of rustls.
Edit: oh, and in such a case you should probably release your own CVE too, else not everyone will get the nudge to update.
At least updating it is easy now - we've put a lot of effort into that process recently.
This theoretical advantage of shared libraries also doesn't materialize, if containers are used.
But I also fear that in this new world of golang and rust projects with statically linked libraries, few people take their reporting responsibilities seriously. Hell, if they did, a serious vulnerability in a commonly used library would result in an avalanche of CVEs.