Disease control is one of the primary tasks of customs and immigrations agencies around the world. This authority was exercised quite prominently in 2020. But it is also exercised pretty mundanely on daily basis in regards to the transport of agriculture that carries diseases of agricultural concern... much to the frustration of travelers with foreign snacks.
From the US Government USCIS Form I-693 Instructions:
The civil surgeon is required to perform specific tests for tuberculosis, syphilis, and gonorrhea. The medical examination also requires the civil surgeon to evaluate for other sexually transmitted diseases and Hansen’s disease (leprosy).
Furthermore it suggests that physical and mental disorders may be grounds for disqualification. Finally, drug addiction and substance abuse generally must be disclosed.
you want to know of any potential carriers and be able to trace potential vectors. plus if you offer socialized medicine you want to know that in order to adjust things like supplies of drugs and coverage for foreign travelers.
Canadian immigration wanted my full medical history for Permanent Resident status, and there was a medical check, blood work, and a chest xray for TB. I was in the US military with injuries from that, and they asked for all of the paperwork.