It is a fundamental contradiction - the perks of standard employment is exactly what makes it more expensive and less dynamic. You can not solve this fundamental tradeoff by introducing some new classification - whatever classification you choose, you'd have to place it somewhere on the spectrum between complete isolation (like ads board having nothing to do with advertised businesses) and complete integration (like full-time union employee).
Whenever you place it, it would be a tradeoff between the interest of the employer, the employee and the consumer. In ideal unicorn-rainbow world, the optimal points would be decided by a free market. In real world the fixed points would probably be negotiated by courts, lawmakers, unions and brazen new companies like Uber finding new optimum spots on the spectrum not explicitly prohibited by the regulators. Of course, the regulators can prohibit those spots then, and that's what is smart for Uber to fight - without it, they're back to existing spots and then what's the point in them being there?
But there's no need for it. These companies not wanting to pay people what the law requires is not a need.
"But I feel they are also not a regular employee."
Why not? Many of the things people cite (get to choose hours, use own equipment, etc) are things that many regular employees also have. How many of us here have flex time?
"It gives both sides rights under the law."
What rights would the employees have under this law? Would they get a minimum wage for the hours that they're logged into the app? Would they get vacation time? Would they get sick leave? Cause unless they get more than they get now, I don't see how this would benefit them.
If the companies can convince the people to want a new labor classification badly enough then they can get it. Of course things will swing back if it turns out to be crap that is bad for enough people and good for too few.
The arc of progress is long.
People sleeping in their cars in between working at an Amazon distribution center or driving deliveries don't want a new labor classification. They don't want to die in poverty and are just trying to survive this ceaseless assault.