Or is this something you came up with?
As requested by the original poster, it doesn’t scale.
I expect a lot of that is due to the referral being familiar with an already ensconced employee, as well as the referrer being incentivized to ensure the referral's success.
If you ask for single referrals, how do you combat the problem of people just recommended people based on friendships and not actually work quality?
Networks all overlap if you search deep enough, ask Kevin Bacon. For good-enough talent and starting with random nodes, yeah, you'll probably not overlap. But there's a few dozen people of top talent for any particular role you're looking for, so by the time you iterate to the top of the tree, you really do get a lot of repeats.