That is by design. Look up the Taft-Hartley Act. Secondary striking is a forbidden labor practice in the United States. Any doctor's union that orchestrated one would be in hot water legally. It would essentially have to be a collective action orchestrated by distinct individuals with no legal entity providing any type of war chest.

To be clear, I believe at least that section of Taft-Hartley is arguably unconstitutional, and worthy of getting civil disobedienced hard. I just don't see it as likely to happen in such a way as to be effective in facilitating change. Add on top of that the onerous burden of medical school debt, and I don't exactly see many being willing to make that choice.

Okay, but the point is sort of that doctors are not in fact blameless for the system that they helped build and continue to participate in.

Like sure, they aren't solely to blame, and it would probably be hard for individual doctors to successfully push for systematic changes, but the flip side to that is that they don't get to say "Oopsie doopsie, it sure isn't great".