The platform that needed to do this, if it were to happen, was LinkedIn. It is naturally a centralizing node, as you put it, that aggregates a lot of recruiting / talent search.

If LinkedIn had used its position to charge subscription fees of its users, not its recruiters, then it could have used that to effectively unionize its entire userbase, across a variety of employers and industries.

But Microsoft owns them now. Never going to happen.

For what it's worth, I don't think it's a good idea (Israel has it's country-wide union, Histadrut, and it's one of the poorer examples of unions), so I'm just pointing this out.