Well it is within their rights, in the hypothetical scenario being discussed where the law was opt-in rather than prohibition.

The argument that "if you don't like it, you can go elsewhere" has been shown to work extraordinarily well when it comes to businesses choosing to go elsewhere rather than serve high crime neighborhoods. In fact it's a big part of why people from those neighborhoods lack opportunity.

Another way of looking at it is that your counterargument to 'business just does what it wants with no regard to the needs of consumers' is 'business just does what it wants with no regard to the needs of consumers.'

You're not really helping your own case here. Especially as you're basically using an example of a case whereby having the state not act in the public's interest by addressing the high crime problem, it leads to poor outcomes for the populace; actually justifying the prohibition in the interests of the public's privacy in general over the freedom of private individuals to create a facial recognition based privacy free zone through their own volition and recognizance by leaving contractual acceptance of facial recognition based programs and data sharing open in much the same way as functioning and effective law enforcement prograns are justifiable in maintaining public safety.

Those neighborhoods lack opportunity because they lack funds and have ethnic names and or faces. When the same resume gets a fraction of the bites when you put the name Jamal on it vs John its pretty easy to identify the issue. Furthermore I don't think disallowing facial recognition is going to materially effect the services offered in a city so this seems like you shimmed it in there.