Eggs store very well when refrigerated and are naturally optimal in terms of physical volume. Buy eggs in bulk and store them in a large mixing bowl or other round container in your refrigerator.
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It is not egg specific. The countries that wash their eggs have atypically strong standards for bacterial contamination hygiene in food processing. Many food products from Europe are prohibited from import into the US due to insufficient safeguards against bacterial contamination during processing. There is an entire business where Scandinavian factories process food from distant parts of Europe to satisfy US food safety requirements for export.
As a general principle, the US does not create exemptions in food processing regulations on the basis that the existing process is "traditional" or has a long history. Many other countries do.
In Europe, poultry vaccination against Salmonella is the preferred method. In most places Salmonella occurrences are exceedingly rare.
In general, Europeans believe that USA has atypically weak standards of food safety and that all the cases when certain kinds of European food are prohibited for import into USA on grounds of food safety are just cover-up stories, because the real reason is to avoid competition.
It is weird that USA has a phobia of vaccines even for poultry, because in this case there is no doubt that vaccines would have prevented the great financial losses caused by bird flu.
US eggs are generally vaccinated against salmonella and washed. The vaccination part isn't mandatory but it is cost effective so producers do it anyway. The effectiveness of the salmonella vaccines is middling at best and unpredictable -- eggs are still a major source of salmonella outbreaks in Europe. The benefit of washing eggs versus vaccines is that it produces a reliable result whereas the vaccine effectiveness has high variance. Also, this isn't a "European" thing, some parts of Europe also wash their eggs for the same reason. The US only started washing eggs in the 1970s, in a successful effort to reduce salmonella incidence.
Salmonella vaccines that work consistently and effectively in poultry are still an active area of research, it isn't a solved problem.
Regardless of what you believe, US food regulations regarding bacterial contamination are significantly stricter than Europe outside of Scandinavia. There are a number of well-known cases where European producers modified or upgraded their production processes to meet US sanitary requirements to enable exports. Scandinavian countries notably don't have to do this because their standards are similar to the US.
There may be other dimensions of food safety that are better in Europe but mitigating bacterial contamination is famously not one of them.