I have done gig work for over four years and my experience suggests that a broker model is effective. I don't know how to develop that outside of the niche where I work, but I am concerned that the focus in your proposal on the amount of the cut taken by the middle man is the wrong framing.
I don't care how much my virtual employer tacks onto what I charge for my work. Yes, it is possible for me to set my pay rate from my end and the person hiring me sees a different number from their end because the service tacks some amount on to covers their expenses. I am very okay with them making enough money to pay for the full time employees that run the service (and other business overhead) so there is a virtual marketplace for my work.
My concern here is that your focus or framing of the problem space will mean the service is not sustainable because there is no inherent mechanism for making sure the service makes enough money to pay its own bills.
I would very much like to see more services that empower workers to set their own hours, choose their own tasks and set their own pay. But they need to be designed such that the service also makes enough money or it isn't sustainable. It will wind up a tragedy of the commons if everyone feels like "100% of that money is mine because I earned it and the middle man does not deserve a cut."
So, I think you probably need to rethink that framing.