3 months expiry time was a deliberate choice to force users to automate the process. Ideally you would have a central store with a letsencrypt client, and all your actual web servers periodically fetch their certs from there.
That's great except the web server (except apache/nginx) needs to be restarted to load new certs, which isn't ideal for production. Many cloud hosting providers don't have an automated way to update certs, which makes it more tedious.