You CAN have it both ways. We can still hold the business to requirements that we set, that represent a baseline of public acceptability, with or without medallions.

"The free market" isn't an answer to everything. We decide as a society that some forms of market pricing are not allowed. For instance, I can not pay children to work for me. I can not pay a woman less than a man. I can not pay an old person less than a younger one. I can not refuse service to someone who has a disability. These are social choices that we make, and I would argue that we SHOULD make, to restrict the free market in ways that benefit society as a whole.