You do realize this is more or less how PageRank worked? Seed of trustworthy domains and who they link to propagates the trustworthiness. This is a take on the idea where it'd be people (not really, still a source) and chain onwards.
I had a similar idea (also, please take it) for online comment systems. Seed of people and who they invite is who they vouch for. The new invitees get to invite more etc. Now, and keep OPs suggestion in mind as well, that's the easy part - here's where it needs to go... If someone messes up, account gets banned and upchain (two levels let's say) gets a notice. Upchain gets one more notice and the whole chain's banned. One notice clears out in half a year or so. Two never. Yellow/red cards for the teams on the internet. One's always at fault, but whole team suffers and is responsible.
What incentivises me to be active and commit time and energy to the site knowing that at any time I could be permabanned by the behaviour of someone two levels away whom I've never even heard of? That's worse than Twitter banning you for some rule break, that's Twitter banning you for someone else's rule break.
You might say that would make you think thrice about inviting people, and yes it would - what incentivises anyone to invite anyone, ever? What makes your system different from a small group of friends making a private invite-only Discord/IRC channel/etc. and keeping it exclusive right now?
I had a similar idea (also, please take it) for online comment systems. Seed of people and who they invite is who they vouch for. The new invitees get to invite more etc. Now, and keep OPs suggestion in mind as well, that's the easy part - here's where it needs to go... If someone messes up, account gets banned and upchain (two levels let's say) gets a notice. Upchain gets one more notice and the whole chain's banned. One notice clears out in half a year or so. Two never. Yellow/red cards for the teams on the internet. One's always at fault, but whole team suffers and is responsible.