There's a few problems with this. Two I can identify right off the bat:

1. Just because you're passionate about something doesn't mean you're good at it. I don't want the William Hung of medicine doing my surgery.

2. By artificially limiting the supply of doctors you are increasing demand and salaries (I agree this seems morally wrong a priori/prima facie, especially for something like health care that is a public good). However when the salaries drop then you reduce incentive for smart people going into the field, which has already been happening in medicine for decades. The top of the class that would've become the brilliant physician in the 20th century is your 21st century finance bro. AKA brain drain. (See also point 1.)

I do agree that it is wrong for people to be unable to pursue careers due to the misfortune of their station of birth. I don't know how to fix it other than funding public education.