Earlier quoted context omitted.
When I can use Let's Encrypt to get a certificate in production without running anything on my production web server, I'll consider it. Right now, StartSSL validates my domain via email and I only have to touch it once a year, not once every 3 months like Let's Encrypt.
Cert rotation every 3 months is a feature, IMHO. It encourages you to automate everything related to rotation.
Automating this simply means that if someone hacks your machine, they also have full access to generate any certs they like.
I don't consider this a positive thing.
You can separate the generation onto another machine, but it's much more complicated, and the default install is not that way.
I have yet to hear any useful reason to rotate the key.