That argument goes both ways:
Should your employer be able to have you on an exclusive contract with a salary so low that you cannot pay your own bills?
Probably not.
The fallacy in your argument is that you're assuming that people like to work. They don't, they do it out of necessity.
An Uber driver doing DoorDash or Lyft between Uber work would be working for a direct competitor, whereas an Uber driver doing errands that require a car from TaskRabbit would not be working for a direct competitor.
When the company fights hard & dirty for decades to classify you as a contractor to externalize the majority of the costs in their business model? Yes.
https://en.wikipedia.org/wiki/2020_California_Proposition_22
I did not know this. Is this verifiable? I thought the whole reason Uber and other “gig” businesses work is because they can pay piecemeal and not have people classified as employees. There were multiple high profile court cases and even attempts to legislate that Uber drivers are employees, but I believe in the US they are still independent contractors, hence they can work for whoever they want, whenever they want.
But what is your apparent assumption that Uber, dorodash, or any other employer owns your body or time. Frankly, that's both a holdover and also a bit of a crack that reveals that what we call slavery, is really just exploitation and abuse and it comes in many forms. Today it takes many other forms, but one of them is what you may unintentionally have internalized, that when you are "working for someone" you are effectively owned by them and you are not free to do anything but what you are told when you are "on the clock", like a part time slave, only with worse benefits.
It's an odd characteristic of seemingly all of humanity to varying degrees, but for whatever reason, one set of humans is not only exploited, but often even participates in their own exploitation (be it the "gig-economy" types or the corporate cheerleader types) while another set of humans enjoy the fruits of that exploitation and facilitate it with things like abusive, narcissistic manipulative language like "freedom of choice" and "democracy" and "gig-economy" and any other of the manipulative, word-smithed terms and buzzwords the PRopaganda people come up with.
They can answer support calls too.
Despite getting an Uber hourly wage many game the system by taking DoorDash and Lyft orders while on the job.
Should your employer tolerate you working another job while you are being paid to do yours?