Use of a CA (private CA would be my thought in this case) gives you greater ability to manage certs without needing to manually revoke and the ability to verify authenticity. You’re already doing most of the work to run a private CA, TBH. Just, instead of signing from the machine, you add your private CA’s intermediate cert to the trusted CAs on your hosts, and generate CSRs on your new hosts for your CA to sign.
Signing from the machine that uses a cert gives it greater authority and increases the “blast radius” if it gets compromised.