The thing is, I really don't understand how this is getting such vehement responses on both sides. In no way is one system clearly better than the other. They're just two different systems. It's like, the question is: "Is the point of the game to win, or is the point of the game to finish in as good a placement as possible?" Both are reasonable arguments, and there's no way that one is just 'clearly' better than the other, or that either of them are ridiculous. Having a point structure does not make it non-competitive, it just makes it different.
If you look at something like auto-racing, they give points for how well you finish, not just where you place. But there are other sports where all that matters is who win. Off the top of my head, I can't think of any sports where there's a field of participants (i.e., it's not head-to-head), where they don't give more credit to 2nd place than 8th place. That doesn't make such a system 'wrong' or 'unreasonable' though. Which is better than the other, is just based on what people think it should be. That's really what matters here. Which prima facie makes nobody's view ridiculous, though you can of course prefer to NOT have that.
The thing with dominion is that this makes more significant gameplay changes, probably, than you'd see in other things. Particularly in the endgame. Again, it's not that one way is right or wrong. How can you say that playing for second is wrong? How can you say that going all out for a win is wrong? Strategically, it's all down to how the tournament is set up. Which isn't clear one way or the other.
I personally advocate for a points system, but one which has disproportionate favoring to the winner. Because I think that playing for a win is an important aspect of the game, and I think you should take the risks, particularly strategically. At the same time, I feel like 2nd and 4th shouldn't get treated the same. There's also then the issue of weird endgame behaviour/collusion-y stuff. Having winner-take-all encourages this more than a point system, because where this really comes up is in situations where it's not possible for a player to win - then they can do anything to throw the game to one guy or another, with no negative repurcussions for themselves. If 3rd is better than 4th, then this would only come into play when 4th place can't possibly even get 3rd, which is going to happen a lot less than 4th being unable to grab 1st. So this is another reason I prefer some point system.
The 'it's harder to set up' thing seems to be a weak argument to me, because it's not much harder to set up, and, more importantly, the people who would be doing the setting up seem willing to do this little extra.
So I would advocate something like 6/3/1/0. There's also the issue of the odd 3-player games, which I would probably have as - everyone plays four player games, the odd people out get buys, or probably preferentially, quasi-byes, i.e. 1 person odd gets a full bye, 2 people odd play a 2-player, where (if we assume a 6/3/1/0 point system for the moment), 1st gets 6 and 2nd gets 3, 3 odd people play a 3-player where 1st gets 6, 2nd gets 3, 3rd gets 1. But it's a bit of a thorny issue - someone is getting the better end of a luck stick, no matter how you slice it.
But more than this, I advocating trying to set up whatever point system to match what will actually be at nationals as closely as possible.