The best jobs and the best candidates for jobs will both be placed privately.

I realize that the plural of anecdote is not data, and that you aren't arguing the contrapositive. But I have a couple of data-points from the last few years that make me believe both directions are not necessarily tautological.

In the direction of placed privately -> best candidate: a company I worked for some time ago had a developer who was placed privately. Specifically, the developer already knew another one of the developers at the company, and came with a glowing recommendation. This person was hired somewhat before the time I was brought on, and as a result, they were well-entrenched by the time I arrived. This would not have been a problem, if this person weren't one of the worst developers I have ever worked with. I wish I could provide more evidence, but it would probably result in both a breech of NDA, and also enough detail that someone on here might know who I was talking about. I've known other people who have had similar experiences of incompetence brought in by some insider repaying a favor of work done earlier. Suffice it to say that there is plenty of offal out there that find themselves insided into companies assuming roles they ought never have been employed doing.

In the direction of best candidate -> placed privately: there is always the story of paul on here joining Google. I'm sure plenty of other stories have been recounted of talented people throwing resumes over the transom, and managing to get someone's attention on the other side. For my own anecdote, one of the best sysadmins I've known in my life managed to find his way into the company I was working at on the basis of a cold resume submission. Nobody knew him, and he was just another name in a pile of resumes; but, it was a pile of resumes that a couple people with a reasonable degree of cluefulness were given to read through, and this sysadmin stood out even on paper. Had we punted him in favor of someone privately placed, I'm suspicious that we'd have been in a much better place.

I realize that you are plenty talented, and am not casting aspersions your way. But there are plenty of hires that are the product of favors of favors, where the biggest favor the middle-party could've done is to never have introduced the company to the candidate in the first place. That's the trouble with favors, though; it is difficult to not be willing to make the connection, because it can bear a heavy social cost to have to say no to a friend.

I'll admit I might be a bit more sensitive to this now because I'm at a small company. A bad hire who was brought in on a favor could send the place into financial pain with maybe a day or two's worth of misguided exuberance. I don't know of someone internally earning social capital for themselves with that as a potential expense is a worthwhile trade-off. I'd rather keep the roadblocks up regardless of how the candidate is sourced.

TLDR summary: Sure, listen to and harvest from your connections, but realize that they have their own interests which may not necessarily align with yours or your corporations, and vet the people you find from them accordingly. The candidate you find or are pressured to hire through the grapevine or a favor may not be nearly as talented as patio11.