After all, you magically get your Victory cards back if you "trash" them, so why not Coin Tokens? Because cards are tiny, and Alchemy is an older set - that's what it looks like to Greg.
Because that's just how the card works. Arguing that it's not fair to use Coin tokens or whatever is just playing with the scrub mentality. Maybe Greg is a scrub, but that still makes him BAD instead of good.
What about Masquerade and Ambassador? They're from older sets than Alchemy and can cause much more harm to the Possessee than spending Coin tokens.
Possession is a weird card with some power cases. I still think that Greg isn't just "bad at Dominion" just because he would have made different design choices than Donald in retrospect. Of course he's less likely to win if he doesn't play to full effectiveness within the confines of the actual rules, but that could have easily gone without saying.
Maybe Greg would prefer to play house rules, where card-passing and such aren't allowed on the same board, and the coin token interaction modded as described. But maybe he's playing on Goko with close friends and taking it on good faith that people will play the agreed-upon "house rules" anyway. Bam, edge case.
(Most likely you just wouldn't buy Masquerade or Ambassador on a Possession board, and coin tokens would similarly be a liability. The coin token case would "feel" more balanced and less hard-countered on a Possession board with the small rule tweak, though - and even with the change, they would still be a significant liability.)