Don't doctors have unions in those systems also.

Yes they do! Unions though aren't the reason for the lack of cheap care, after all each party involved in a private system is incentivized to gouge as much as possible due to a lack of collective safety nets.

> collective safety nets.

as in losing jobs to ML algorithms ? What would the point of a union then :)

Is this the hypothetical future where every job is replaced by a ML algorithm? In such case, you better hope there is some form of collective safety net for you ;)

> Is this the hypothetical future where every job is replaced by a ML algorithm?

No. we are talking about doctors in specific.

Your original point won't stand if everyone in the world is replaced by AI.

> If only you guys had universal healthcare

There would be no private insurance through their employers if no one has a job in first place.