Not can’t at all but the licensing hurdles can be really difficult if they didn’t go to med school in the US, as I understand it. Even from other countries that are clearly pretty good at educating & licensing doctors.
In Canada, the “brain drain” of Canadian-trained doctors to the US is very well known. It’s comparatively easy for Canadian doctors to start practicing in the US (much easier than the opposite).
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My current two doctors appear to be native speakers of English, but the previous four or five were all clearly from the Subcontinent or East Asia.
Note that I'm not criticizing them in any way... they were all perfectly fine doctors. I'm just wondering where OP is from that there aren't tons of imported doctors on staff.