All of these things can mostly be tested. When I donated regularly in the UK after being in the southern US, they screen me for west nile virus but still take my blood and use it.
Blood is tested for disease, but the false negative rate for each test is its own risk.
If you got blood from an addict living on the street engaging in prostitution and tested it, would you trust that blood?
I wouldn't.
The UK also has a wait time for many countries including Mexico.
https://my.blood.co.uk/eligibility/travel/article?id=47&titl...
Granted it’s shorter, but there are longer wait periods depending on the country. It’s defense in depth because false negatives happen and some viruses take time to show up on tests.