But you're right that the super market displays them on ordinary (not refrigerated) shelves.
You don't actually need to refrigerate eggs in the US if you never eat them raw. I have not refrigerated mine in decades - I buy them, then just leave them on the counter.
Also you can raise them in special trays that remove both the eggs and the waste immediately, reducing how much gets on the egg.
The EU forbids washing to encourage producers not to have salmonella in the first place, the US prevents the salmonella by washing. In practice the EU vaccinates their chickens against salmonella. Around half of US producers do as well.
US food regulations require stronger mitigations against bacterial contamination than most countries pretty consistently. If you look at the long list of foods prohibited for import into the US from Europe, it is almost entirely due to insufficient mitigation of bacterial contamination. This largely revolves around traditional food processing techniques that don’t pass modern food safety standards but which get an exception in Europe for being “traditional”.