You've now turned a moral willingness-to-help problem into a logistical and coordination problem.
What you suggest requires entire organizations to execute properly. These organizations do exist, such as Doctors Without Borders.
I don't think your original claim is fair, which amounts to "any surgeon who does not participate in Doctors Without Borders is just as bad as a landlord who evicts a family during winter".
What do you think we owe to one another, philosophically?
It's not about what I think. The post I replied made the assertion that individuals don't turn people away like corporations do (essentially).
My point is that individuals choose not to help others constantly. Every time I see a homeless person, I don't offer them a couch to sleep on. I could, at least once, but I don't. We all do that, most days multiple times.
And yes, that does apply to doctors who don't volunteer services. It applies to me too and, I bet, to the OP as well.