Both of your observations are due to constant relentless cost optimization within the postal system. Local post offices, for the most part, don't postmark mail at all. Everything gets batched to the regional processing center where it goes through the big automated sorting machines.
I seem to remember a "local only" box in the town where I grew up but that hasn't been a thing for decades now.
A friend lived in a smaller town where mail was processed in the nearest larger city (in a neighboring state). But, if you needed something sent to (most of) the rest of the state, it was faster to have it processed in a different city in the other direction. They had a specific drop box for that, which cut delivery from two days to one. I, living in the second city, was stuck with having my mail routed out of state to get to him.
I seem to remember a "local only" box in the town where I grew up but that hasn't been a thing for decades now.