Is this a new development with namecheap? I currently have a domain with them that is set up with let's encrypt.
I haven't touched my site in a long time now but visiting it now shows https.
Apparently not, but I only just noticed after their free 1 year trial of SSL certs expired. They're listed on the Let's Encrypt site as having no plans to support and the source is pretty hilarious:
https://community.letsencrypt.org/t/web-hosting-who-support-...
Yes, you can set it up manually, but you have to do it every 90 days as opposed to having it automatically updated in a supported hoster.