With certificate pinning, that is not a high risk.
Also, using Let's Encrypt doesn't stop you from certificate pinning.
There are far too many ways to self-DoS accidentally with HPKP. Also, an attacker who briefly gains control of your public DNS or web server can DoS a hostname semi-permanently.
For service-to-service stuff and APIs the number of TLS clients that respect pinning is approximately zero.
Either way, the other problems remain, and running an internal PKI is really pretty easy.