American eggs are required by regulations to be washed. This includes wholesale.

European egg producers are not going to invest in washing machines for a temporary market. America needs to either accept a breach of their own regulations and wash the eggs themselves, or offer a price that makes it worthwhile for the European producers to follow American regulations.

Overall, with potential tariffs and additional cost for transport and washing, it seems like a bad solution. It would probably be easier for US to produce more eggs themselves.