How about non 0-cost Cursed cards can be discarded manually and individually by the discard button ?
Yes, cursed is quite overpowered: you reduce opponent effectiveness by 1/8 down to zero once their deck is full of cursed cards. Then it's another 8+ turns before they're out of that, increasing effectiveness up by 1/8 every time they play out a cursed card - more than enough time for their opponent to get an unbeatable lead.
Maybe the "replace opponent hand with cursed card" should be made harder to enact.
Maybe Holy (and perhaps Aqua and Nature) should (give a chance to) banish cursed cards in hand.
Maybe Wish (among others) should be able to replace all cards rather than discard and re-draw (which fails to work on cursed). Or there could be a higher-priced common that does this ("Fervent wish"). The price to the one who plays Wish is that they lose any good cards they'd have liked to play... and undoubtedly they will have to do that several times in the course of a game, which still seriously hobbles performance.