It’s of course more friction, which in itself is good to avoid spam/bots, but over time all of that can very likely be automated
> [...] would be roughly proportional to the strength of the friend network connecting them.
Easy to do, easy to implement but hard to bypass. Also it tells me something about the network that is not vying for a slice of the attention economy and isn't going to do everything it can to keep me on the site.
But it wouldn't actually work well. It doesn't even need physical invites, keeping track of the invite graph is a great way to kick scammers out. It works. It's been demonstrated to work well since at least 2004.
The reason social media sites don't do it is not that it doesn't work - it's that growth trumps those concerns. Making onboarding as easy as possible is more important than keeping scammers out.