There's something there, although I've thought a lot about this too and here's my free idea for @vs2370 or LinkedIn: let me control how many job opportunities I receive (unlimited, 1/day, 1/week, 1/mo, etc), then auction off those slots to companies/recruiters.
Really, what I want is the best offer every so often to keep my head in the market, and (I assume) the amount recruiters would pay to contact me is basically meaningless to me but nontrivial at scale for the platform.
Or maybe Dutch auction and send me the top 3, then I can ignore them if I want but I can at least pick my favorite(s) to give some signal back upstream for what kinds of jobs I might actually be looking for (or let me "thumbs up" any that are particularly interesting, etc), even if I don't actually respond to that individual contact.