I would think that almost any airfield would be virtually dead in any "bad" weather, so a lack of PPR to exercise the filed alternate option should not be an issue.
I don't understand this PPR/PNR thing.
Why can't people just arrive whenever they like and land on it?
Because that's the way it is. America doesn't use PPR. It's a largely European / 3rd World thing, tied up with job creation, etc.
If an airport is having capacity issues, just build a new runway?
Very tricky planning-wise. But very very very few GA-accessible airfields have anything remotely resembling capacity issues.