You’ll never get the recruiters to participate, because their companies will never let them. LinkedIn is corpo hive-mind central, friendly to corpos first and foremost. What you’re proposing wouldn’t be friendly to corpos, inherently, so they’ll never join, and they hold the strings because they are the ones with jobs to offer.

You’re literally asking how to take the corporatism out of LinkedIn when that is precisely what allows it to exist. Why would any company participate on a platform that gives workers the advantage? Hint, they won’t.