Ok the new wording is clearer... but my second question remains... why bother having them reveal their hand? Limiting which cards you are allowed to trash from the supply just feels arbitrary; and it will be very random. It doesn't seem like it should be an attack; it doesn't hurt your opponents at all. Allowing you to trash 1 card from the supply per opponent instead of always just 1 card also seems like a strange way of scaling with more players.
I believe getting to choose which supply piles decrease will deplete supplies of their strategy, incite end conditions more in your control and address the valid concern for not depleating cards from the supply while using the card. Choosing from oponents hands also scales better then choosing one of your choice, would it be better to choose a supply pile per player without the reveal mechanic? I don’t think so. I think if I did that it would be too effective too quickly and diminish clearly sought supply piles for other strategies too soon and too consistantly. It shouldn’t be that guaranteed, but still happening.
Just choosing one may be better though... imagine a 4 player game with one of these played by each player one round... 12 cards poof.... yeah...
One card actually scales better... updating OP