The distinction you draw at the top is the one that matters most: a required field proves someone typed something, not that it is right or that anyone checked it. That is still useful, but it is a completeness check, not a quality check.
In practice I would keep the required list as short as possible — only the fields someone will actually act on at that stage, like a close date and a decision maker before Proposal. Every extra required field is an invitation to enter a placeholder just to move the deal forward, and then the forecast is full of dates nobody believes.
The second check you suggest is worth doing too, especially for imports. A deal that arrives already sitting in the wrong stage with blank fields will never see that stage prompt, so a workflow catch is the only backstop. And the Closed won point is worth testing in your own account — if deals can jump straight there, that is where the missing information hurts most.