They are not developers - they have no rights to write commit and promote code but they are good enough at reading it to not be helpless when something breaks down and they need to take a peek what has changed recently in the codebase and stuff like that.

I on the other hand have no admin rights (only read access) but I know enough of out network and ops structure to be able to make an educated guess when something is behaving strange.

So if it hits the fan they could probably patch an emergency bug and I could fire up some VM instance. It is not about wearing a lot of hats, but being able quickly to put on a new one if needed.

Try working on small teams, very small teams. There is no way around it, you must wear multiple hats, and those hats grow/change over ones career.