Rabbaim, Yidden who die in a hospital create tumah but it doesn’t necessarily spread through the entire building. There are many complicated halachos about tumas ohel. That being said, you are correct that kohanim generally shouldn’t work in a hospital setting in places like NY and Israel where there will inevitably be Jewish corpses over time. But there are exceptional cases where the part of the building he is working in does not get tumah because of the layout of the building, where in the building people dies, etc. Also, to work in a hospital in a neighborhood that has very few Jews or to work in an office building where there are no seriously ill patients is another story. (Of course, getting through medical school without being mitamei is another story as well)
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