Also the "all immigration happens overnight" plan is obviously a bad way to handle things. That lag wouldn't be a big deal if we 'merely' instantly doubled the rate we issue green cards and ramped up from there, just to make up some numbers.

Definitely.

>I could see it actually helping out with our self-inflicted doctor supply problems.

Only if they are overrepresented which they aren't(in Europe at least). You need to actually work hard to convince doctors to come to your country and not others, but with other migrants you need the opposite. Convince them to stop coming.

Well the US isn't Europe and it imports a ton of doctors.

We pay doctors a lot and have an artificially limited supply of native doctors.