Ideally it should be across corporations. I know a ton of people who drive for both Uber and Lyft, depending on who pays better. Thats a critical element - there needs to be a market of companies for people to work for, but they still need solid benefits and protections.
Think of this as a next generation union type structure.
I don't know why this doesn't come up more. People get hung up on whether contractor or FTE fits gig workers better, without ever suggesting there's a categorization issue here that could best be solved with a new category.