They do leave the market. Where did you get that idea from? My parents have extreme difficulty travelling now because they have a dog, but their local dog kennels have been closing down. When the last one went my mother talked to the owner. He said the rise in minimum wage was killing the business. People were willing to work there for lower than the new minimum because they love dogs basically, but customers weren't able to pay the new higher prices. So he had to fold and was quite bitter about it because the government had basically killed his business that he'd spent years building, in the name of "fairness". So all the workers lost their jobs and of course there's a knock on effect on the wider economy because that particular service made it easier to do leisure spending.
But socialists never think about this stuff. They just pretend there are no downsides to central control of prices.