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[theory]

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Well. In 2007 and 2008, and for most of 2009, it went left. In late 2009, Wei-hwa pointed out that it created a political situation when the possessed player had Masquerade in hand in games with 3+ players. You decide to make them pass a good card or not to the player to their left, based on who's winning. If Possession goes to the right then this isn't an issue - you're passing the card to yourself, which is good for you and bad for them but not political. Then when I handed the file off to Jay, he changed it back to to the left because that's more natural.

The Possession story perhaps makes it clear how down on politics I am - I was willing in the end to change Possession just to get rid of that one situation. You can only maximize one variable, so if you want to maximize fun, maybe you will be stuck with politics sometimes. And in general you can't completely eliminate politics from games with decisions. But minimizing politics tends to make games more fun for me and is a top priority. Dominion has politics but sure struggles to minimize it.

And one of the ways it does that is by not letting you pick players to affect. That leads to politics. It may seem an unlikely situation that you happen to know that two players have say Gold on top of their decks, such that picking who to Tribute amounts to picking who to hose. These situations are still likely enough that they're a big negative for me. And I sure don't want to have to avoid making a card in the future that would create a political situation with Tribute. Any potential benefit to letting you pick for Tribute is just dwarfed by these issues.

There are cards in Dominion that can only exist if they interact with a specific other player, and if they're worth doing they specify the player to your left/right. They don't let you pick a player, because that might lead to political situations. I can avoid that problem by not letting you pick and it's so easy to do. If I had such a card that didn't look like it would ever be a problem I probably still wouldn't let you pick, just to be safe.

[theory]

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I agree that there's a downside to attack-to-the-left and such in a game where some players may never attack (I think it's fine in games where everyone is always attacking). I don't agree that it's worse than picking who to attack. If we are picking who to attack, I will be spending the evening trying to convince other players to do things that are to my advantage ("attack Tom, he's winning, man my draws have been horrible, did you see Tom bought the first Gold, ugh, we're not catching him anyway"), rather than, say, playing the game. I hate that. I feel like I'm a good whiner, but it's just not what I want to do with my time.

Whereas if there's an attack-to-the-left card, then I can be sad if I'm sitting next to the guy who always buys that card and happy if I'm sitting by someone who never does, but either way, I make the best of the situation via my strategy in the game, and spend no time on politics.

Dominion currently has a few cards that make seating matter in order to get at information in good-sized quantities. Envoy is an example; we can have the player to your left pick the card for you to discard, whereas having all opponents vote on it or something is just not feasible. It's nice if the player to your left is bad at picking the card for you to discard to Envoy (for the situations where it's not trivial), and sad if they're great at it, but it's not significant enough to have ever made someone ask to randomize the seating order. That is my target with cards like that. If there's ever an attack-to-the-left card, I expect it to be something that wasn't possible otherwise and which doesn't make people demand to randomize seating order.

In general attacking just one player doesn't work in Dominion anyway; the attack has to be three times as powerful as a normal attack, in a 4 player game, in order to be worth buying, and I can't make the attacks that powerful or it's too painful being hit by them. This is also why I don't have anything like a Moat that gives the attacker a Curse; it amounts to attacking that one player, and your attack is very small from your perspective (one out of three opponents got -1 vp, which is like you gaining 1/3 of a vp, ignoring the bit about how it also messes up their draws), but large from their perspective (if they played Witch, the Cursing part was completely nullified by just one player, and if multiple people have these Cursing Moats, you would have been better off not attacking). You're the one deciding to buy the reaction, and don't have sufficient incentive to buy it, and they're the one deciding to buy the attack, and there's a strong incentive not to. So it just makes cards go unplayed.