Is SSH over TLS 1.2/1.3 overkill?
SSH over TLS isn't just an overkill, it's a software bloat / design creep. 


Both protocols provides confidentiality, integrity, and authenticity guarantees, so using two is redundent. And coding for both of them would increase the size of the software, making it harder to maintain software quality, efficiency, and security. 


Benefit of SSH


SSH is already a very good application data encapsulation protocol, and in fact, the most widely used SSH implementation "OpenSSH" allows you to setup your own service running side-by-side with sftp. In my opinion, SSH is easier to setup and have many desireable features for specialized application.

On the other hand TLS carries too much legacy, it has too many options that needs to be supported to maintain compatibility with existing implementations. Even if you implement no support for versions before TLS-1.3, incorporating support for it in code still require considerable amount of expertized skills.