So not only do you have a recipe for cripplingly slow growth, but you also fail to ensure improvement in the quality of submissions. It's not like people are invulnerable to "Dude, c'mon...invite me!" from their friends, hacker or otherwise.
We have a pretty good crowd here now. I think that most of our friends would also be a good crowd, and most of the annoying 14-year-olds wouldn't be our friends.
And this didn't cripple the growth of Livejournal at all. You only get one invite a year, but you get it immediately on joining. I invite you, you turn around immediately and invite someone else, who invites someone else, etc. The 1/year rule is meant to make me careful about who I spend my one invite on.
This is how Livejournal used to work, and it resulted in everyone knowing at least one other person, which was important for a community site.