It's not like possession makes you actually lose a turn. It's a card that "feels" a lot more unfair than it is.
It may be a fair point. But, in my limited Dom. experience, I can already tell that (1) it is really fun when you build a great engine, and (2) it is not at all fun when your opponent has built one, since it means you are just sitting there for an extended period, just waiting and waiting. Then your turn comes, you take 15 seconds to finish, and then there's another 3 minute waiting period, as your opponent again cycles through her deck. (As I said; it's really fun when I'm the one doing the cycling.)
Ten times worse is when--during these long opponent turns--you have to respond at various points. To pass a card for Masq., for example. I've been well ahead in a few of those games and still wanted to resign...it just wasn't fun.
And for whatever reason, Possession just pushes those psychological buttons for me. I'm willing to play with any other card. But just not Possession. File it under "Life is too short." :-)
If it ever happens to show up in a game (and I have marked it as Unfamiliar, to minimize this), I ask my opponent if we can agree that neither will buy the card, and that I am happy to resign right there if that's a problem. Voila! Problem solved.