Possession is the most hated card among casual players. I would drop it because of how much it turns people off.
It goes beyond hatred. Given all the non-card assets that have been introduced in Guilds and adventures, Possession is very much an attack now, but it is not called an attack and cannot be defended against as attacks can. This is a mechanical problem that cannot be addressed without a major rewrite of the card. Best to get rid of it.
IGG is a much worse "pseudo-Attack" than Possession. Whether Possession has the Attack type or not would rarely matter anyway, since there's only 3 cards in all of Dominion which can prevent an Attack, plus only one or two that would help the Possessed rather than the Possessor (Secret Chamber/Diplomat to make your possessed hand worse and occasionally Beggar). And it's good that you can't trash Squire to gain Possession.
There is one key factor you are missing. By design, attacks affect all other players, while Possession only affects the player to your left. In 2 player, this distinction is meaningless, but in 3+ it is significant. When player A plays a Militia, B, C, and D all either discard or block the attack through moat or lighthouse. When player A possesses, they can can spend all of player B's coin tokens, or turn B's disciples into unwanted teachers, or move adventures tokens to useless cards, etc to damage B's chances, but C and D are unaffected.
By the design of the game, cards that are attacks should have the potential to damage all other players, cards that are not attacks should not damage any players. If cards were the only game pieces, you can argue that possession does not actually damage the possessed player (though there are certainly times where this happens, such as when the possessor discards the possessed players alchemist chain when he could top deck it) since deck composition is unchanged after the possessed turn. In the presence of all the other additions mentioned above, possession in effect becomes an attack that damages only one player. In 3+ player, I view this as unacceptable, and therefore view the card as fundamentally flawed in it's concept. Fixing it is impractical at best. I feel that the card is fixable and should not be part of the game.
