The way this works in practice is that I see a different pay scale than my clients see. So, if I say "I will do that job for X" the client sees "She will do that job for (X + Y)" or "She will do that job for 2X" or whatever their formula is for calculating the total fee. I can absolutely set my own rate. There is fine print somewhere that tells me how much they pad it when billing the client. But it is possible for me to relate mentally and emotionally to "I get paid X" and not care what the service charges for their cut because they aren't taking it out of my hide.
I would be disinclined to pay a service for the opportunity to access work. Because that means I need to keep working X amount to make it worth my while. In this case, I need to do enough work that I am making more money after paying the fee than I could make for less effort by sticking to the free deal.
So, if I can make $100/month without giving you any money but earning $101 or more means you will charge me $20, then I need to make more than $120 every single month to justify paying the fee. That makes it a burden in my mind, not an opportunity. It means I have to be confident that I have the time, energy and interest to do that consistently. It also means you become an albotross around my neck in my mind.
This creates a barrier to entry for treating this like a real job. You cannot ramp up at your own pace, as you see fit. There are financial incentives for many people to treat this as just "extra" income and not an avenue to support yourself. This will harm the long term reputation of the service, as well as threaten it's financial survival.
What I am telling you as someone who makes most of their earned income via gig work is that your stated ideals of empowering the worker are far better served by adding a surcharge to every job that gets charged to the client, not the worker. That is also more sustainable for the business.
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.