I think you're right. The issue with these services is that they're extremely local. Really, only cities will likely really have much competition. That relies on there being separately owned facilities. And even then there is the issue that 2-3 providers never really compete even if they're not colluding...
I honestly think that free market healthcare is doomed to failure. The information a-symmetry, the size of hospitals compared to populations, localization, the degree of specialization, strategic nature of services, and the social externalities are just too great to ever really have a market. But that's just me on my soap box.
Hopefully transparent pricing will do some good at least. I wonder if requiring insurers to share savings in cash would further encourage people to shop around (eg going to the place 4h away to get a 2k MRI instead of a 4k MRI means you get say half the saving [1k] back from your insurer)...