>because I know of no hair stylists nor construction workers that work by only doing the jobs that are allocated to them by a single company yet have no employment contract with that company.

Can't a rideshare driver work for both uber and lyft? Moreover, how much job hopping actually happens for hair stylists or auto mechanics?

For a long time I used a hairdresser (aka barber or hair stylist - but I’m male with simple short hair) who worked at two salons (aka barber shop from the mindset of customers like me) every week. It definitely happens. A typical model in that area (NYC) for hairdressers who didn’t own the salon was to rent a chair at a salon, but they weren’t employees and were totally allowed to do part-time chair rentals at multiple salons at once.

Her contract with my salon prevented her from telling me her other salon, so I had to switch hairdressers instead of staying with her when she stopped working at that salon.

The other hairdresser I switched to later bought the salon from the previous owner when he retired, complete with a rename of the salon from his name to hers. I still use her when I need a haircut and am in NYC. And yes, there are still other hairdressers working there, presumably each renting a chair as she previously did.