HTTP/2 does not require TLS support.
It just so happen that all browser vendors (and only them) decided to not support clear-text HTTP/2, but other clients such as curl, or Java clients, etc. do support clear-text HTTP/2.
However, for server-to-server communication, it is possible to use clear-text HTTP/2, and in fact this is a very common deployment.
It is also unfortunate that popular servers that are used as reverse-proxies or load balancers do not support invoking the back-end using HTTP/2, but that's just an implementation limitation.
HAProxy, for example, allows to offload TLS and then invoke the back-end with clear-text HTTP/2.
If you receive many multiplexed requests on the front-end, you can leverage HTTP/2 multiplexing towards the back-end, saving a lot of resources.
A web page that requests say 30 multiplexed resources to the front-end will need to open or otherwise use 30 different connections to the back-end when using HTTP/1 (or less connections and be less efficient), versus using just 1 when using HTTP/2.
When using HTTP/2 towards the back-end, you are not limited to just 1 connection, exactly like you are not limited to use only 6 connections when using HTTP/1 (these are just browser limits and do not apply to server-to-server communication).
Furthermore, back-end applications that use HTTP/2 features such as HTTP/2 push (albeit now being phased out) would work transparently using pure HTTP/2 communication, while won't be able to use the HTTP/2 features when using HTTP/1 communication towards the back-end.
This is true for any other HTTP/2 feature such as PING frames, SETTINGS frames, etc. all of which are lost when communicating to the back-end application when using HTTP/1.
From the resources point of view, a smart reverse-proxy or load balancer can just offload TLS, and then blindly forward the HTTP/2 clear-text bytes to the back-end -- no need to interpret the bytes in either direction.
There would be no need to parse the HTTP/2 request, convert it to the HTTP/1 format and viceversa when receiving the HTTP/1 response (from HTTP/1 to HTTP/2).
This causes unnecessary CPU burning and TCP connection usage.
So, in principles HTTP/2 towards the back-end is very desirable.
I have worked with clustered systems where HTTP/2 for server-to-server communication was a huge benefit just for the many less resources used across the whole cluster.
The reality, however, is that the most popular front-end servers do not support HTTP/2 towards the back-end (mostly for non-technical reasons), so most of the times you just have to give up and deploy sub-optimal systems.