I started writing a small utility to do just that (and then upload the cert to CPanel using their API). It works, though I'm lazy to make it reliable enough for release.
I must have at least 4 accounts there due to them using client certificate login. Great proof of concept why certificate based website logins never took off.
https://groups.google.com/a/chromium.org/forum/#!topic/blink...
https://github.com/JrCs/docker-letsencrypt-nginx-proxy-compa...
The market is probably (a) people who want to support/donate to LetsEncrypt and (b) people who are ultra-paranoid / strongly prefer less moving parts in ops.
The one major downtime I'm aware of so far (a month ago) could also be a factor: Let's Encrypt is down | https://news.ycombinator.com/item?id=14374933