This is a good point. Some people might get screwed, and not have a better market option locally. Of course, there are other options. If the only retirement home (school/daycare/etc) local to you is horrible, you could always start your own. Or advertise for someone to do so. If you've gotten screwed by someone, take them to arbitration.
You could start your own, but many times that's not a option (lacking the time/skills/capital to do so.) But that doesn't really help the situation. You won't put the bad bussinesses out of business because of the reasons I outlined before.
But this does bring up another point; the free market presumes that there are enough people to do a job or run a certain venture, and when there aren't enough people to provide a certain service, it becomes scarce and the price will go up, drawing more people to the oppertunity and solving that problem. But what is that's not the case? What if there are not enough people willing to provide a service that is needed, and there are simply not enough people to do the kinds of jobs needed? The price will certainly go up, but it won't ever come down and that means a service becomes unavailable to many people. Depending on what the service is, that's anywhere from not really a problem (luxury goods) to clearly unacceptable when it's a service like running a daycare, medical care, running a retirement home, when this is only available to the (super)rich.