At the risk of making a very elaborate "this" post, I agree with all above points.

I've mainly used invitation-only to minimize load or at least to get a better idea of where the pinch points were in where scaling is going to be tricky. It's nice to be able to say "We're operating just fine with 100 logged in users. What happens if we have 1,000 logged in users?" and be able to control that to some degree. Giving each user a couple of invites is going to grow the population (you hope) but not open up the firehose completely. If you don't know how you're going to scale to 1,000 users, you might not want a million users just yet.