Just in case people reading this thread aren’t familiar with the key usage concept, the Let’s Encrypt certs are indeed intended to be used with POP, IMAP, and SMTP servers and should work fine for these applications.
The applications that are forbidden by the EKU policies are other non-TLS uses such as code signing.
Hopefully the Let’s Encrypt client will eventually even have built-in functionality to help you automatically install certs into servers for other Internet protocols, like IMAP servers.