Not a great deal to add to the comments already made on this thread, except to say that I am generally in favour of checking that the engine will run on each selector position before takeoff if possible.
BPF, in his inimitable way, though, makes a couple of very valid points:
1. It's not in the POH, so Cessna either didn't think of it, or didn't think it was necessary.
2. By making the checklist more complex, we increase the possibility of a mistake, and in doing so, we may inadvertently introduce a risk that is greater than the one we are trying to avoid.
So, before adding stuff to the POH checks,
consider carefully if the perceived benefits outweigh the potential risks.
MJ