I can think of a few things that differentiate the FoFF from the generalized “finding the most connected network node” problem.

1. The FoFF algorithm is not actually random. In the network node problem, you randomly select a connection from the current network node to traverse. In the FoFF algo, you let the network node evaluate on its own metrics who to make the introduction to. In particular, you have to hope that individuals won’t have selection criteria that bias them towards investing in less-connected people than themselves. This seems risky: if I’ve been given $10k of free money to invest in my friends, the returns of which I don’t see, then I’m more likely to give it to the poorly-connected friend having a hard time raising anything, than I am the well-connected friend who is sure to raise money with or without me. Maybe this is the result that you actually want, but it’s a different result from finding the most-connected entrepreneurs.
2. Just based on the way you’ve articulated the network node problem, it’s better to make several steps along the network, than it is to pick 3 friends from each network node. That suggests that instead of allowing each person to invest multiple times, they should only invest once. This way, you’re making long chains within particular networks, and are more likely to lead to high-value nodes. But I might be reading into your explanation too much.
3. There network node problem assumes no other ways to see which nodes have how many connections. Of course, the truth in the real world is that there are already selection criteria used in this way. In particular, funds already prefer to invest in startups that have been introduced by another entrepreneur, well-connected people already have an easier time raising money, etc..
4. And of course, as you’ve pointed out, there is a difference between trying to find the most connected entrepreneurs, and trying to find the most likely to be successful entrepreneurs.

All this said, I really like this general idea. I’m only trying to poke holes into it because you specifically asked!

One thing that might be interesting: a venture fund that does seed/A rounds, and as a part of that A round earmarks money for each founder to make a single angel investment. These small investments are several orders of magnitude smaller than the main rounds, so they won’t grow as explosively, and it could potentially lead to good dealflow once those companies get to their first round of VC fundraising. It also begins training entrepreneurs early on how to make good investments.