I think the answer may be "yes" effectively if it leads to establishing companies of contractors but not without side effects in themselves - like most regulations really.
If gig economies lead to working with companies instead of individuals that would lead to two distinct branches.
* A self established one would give more regulatory surface for things like training and background check requirements. Not as easy to sign up before any added regulations. Constituents would get more of a pure cut. The barriers to entry would make their labor slightly more valuable.
* A traditional company which hires employees. They would have a middleman to make signing up easier but likely less flexibility - which doesn't matter as much to fulltimers anyway.
It likely result in a less flexible market with more barriers to entry but it would solve some problems and act as a framework to add more solutions and problems for better or worse. It could be abused to create cartels again or responsibly handle externalities without unduly privileging - it depends on how the tool is used.
Second order effects are likely a labor pool that cannot rise and fall as quickly which would stabilize prices for the labor supply and turn instability into a company liability as they may be left with a choice of paying for idle labor for availability and meeting demand for sure or risking being unable to fulfill demand.
That said I wouldn't be surprised if widespread roll out of these sorts of laws caused a gig economy bubble to burst - especially given how many are doing a VC dumping strategy of losing money on transactions.
I don't really have strong feelings as to what would be the best nor consider myself above an amateur commentator.