What's worse, many of them are monopolies (which is also a non free market).

However they are far from sufficiently regulated (which monopolies should be). Otherwise data caps rip off would have been illegal to begin with.

The question isn't free markets, but effective ones which serve society. Effective regulation is what makes markets.

Economists far more generally speak of competitive markets, which carry numerous requirements, of which neither healthcare nor Internet / communications generally satisfy.

Which is how they came to be regulated in the first place.

I think the language itself here is a problem.

Effective regulation is what makes markets.

More specifically, free and open markets work wonders -- but dominant players seek unfair advantage to eliminate the free and open market almost as soon as it starts working.

Some regulation is required to keep the market free and open to all participants, especially as leading players actively change the rules as they gather more resources. But the critical point is that those same players are far more likely to use regulation itself as an unfair advantage as they are anything else. Government is the biggest stick in the room, after all.

So yes, free and open markets work, and yes, regulation is required to keep them working. But regulations do not make markets any more than speed limits create the interstate trucking system.