Anyone can verify his reserves if he posts addresses. That's the point
Discussion
What addresses? He could post any addresses and say they're his. And if he or the syndicate of massive Bitcoin holders(blackrock, CoinBase etc.). Want to fake you out with PoR they can simply give short term loans to each other to "prove" they have the Bitcoin.
It seems like PoR would need to be done like automated bank runs in Ecash......all at once
Sign a message from them
Sure, that fixes one problem, but what about fast loans back and forth between large holders?
You would see it on chain
You would see something on chain but not it could be made quite murky with coinjoins or payjoins or any number of clever and cheap techniques. Also you would have to know with certainty who owned the UTXO it came from. Otherwise they would of course just say it was there and they were consolidating
Psudonimity is pretty powerful