Those aren’t really analogous. Doctors aren’t pro-vaccine because it’s good for their business interests. They’re pro-vaccine because their community agrees that they work and are produced safely. In the case being discussed, the argument is the anti-rent-control folks are letting business interests drive their argument.
What do all businesspeople have in common? They are trying to make money – and that's all they have in common. So we can expect a pro-business publication to advocate for policies that funnel wealth to businesses, without much regard for anything else.
In contrast, the one thing all doctors have in common is that they try to keep people healthy. So we can expect the medical community to advocate for policies that accomplish that. Of course there are doctors who could potentially have a conflict of interest between getting more business and doing their job correctly. But then we can still expect both factors to play a role, i.e. very few doctors would focus purely on getting business. And many doctors don't even have that conflict, e.g. employed ones whose job is secure.
If vaccines harmed people's health while benefitting doctors' bottom lines, we'd see a split between employed or ethical doctors vs unethical self-employed ones. It's inconceivable that there's a consensus among doctors for a policy they believe is harmful.
Anyway, I doubt vaccines even do increase demand for doctors. Administering them is cheap (~5 minutes of a nurse's time), treating the diseases they prevent is not.
