They don't keep a name-list or seat-list Premium Economy right?
Wrong.
It's worth watching what the cabin staff does and talks about during the boarding and take-off preparation. One of the things that you can't overlook when you sit in front of a (smaller) plane is passing the passenger manifest by the ground staff to the on-board crew. This is pre-requisite to complete boarding. It might be handled through apps in some airlines these days but it has to be passed and confirmed for the plane to close its doors.
Then the crew discuss what kind of "special" passengers do they have and how many of them. Usually premium is handled by a different part of a crew, so they'll be fully aware which seats should be empty. I remember overhearing a discussion like "we have two infants, 5 premium and 3 business on-board today" when I was sitting in the back of a plane.
Finally, the premium economy usually has some kind of complimentary meals even on a short-haul flights. On long-haul the meal offered is of a better kind than that served in Economy. Those are also carefully counted so it will be obvious that something is wrong.
I have also personally witnessed once a person to be pushed from a premium to economy seat (she was evidently trying to "upgrade" her flight the way you describe) and once a person being requested to get back to theirs seat within Economy. So apparently crews are cautious about such things.
All the flights I'm referring here happened within Europe, on-board of different airlines though.