But how many points will the Rebuild player have taken off the board by the time you have Possession and a good HP stack?
And that's not a rhetorical question. I can see that strat working. But I do wonder if even that is fast enough. I think it would be in a Shelters game, but with Estates, I don't know.
It's strong in a Colony game, where you have extra time and each possessed Rebuild gets you 6-11 VP. In a Province game, even with Shelters, I'd need to see a lot of support for Possession in the kingdom. I wouldn't even consider it if Rebuild has Warehouse or Scavenger or similar to help it.
Compare possessing a Rebuild player to possessing some other player. You're playing most of your Possessions T10 or later. So possessing a generic non-Rebuild deck is worth, eh... something a little less than a Province on average. On the other hand, Possessing a Rebuild deck is worth maybe a little more than a Province. And there's some extra value in the fact that the Rebuild player can't defend by over-greening.
Hand-wavily, I'd estimate that Possession against Rebuild might be as much as 50% better than Possession against some other deck. It's definitely not twice as good. On the other hand, Rebuild is going to change a 16-turn game into a 12-turn game, which cuts the Possession-playing opportunities in half or worse.