Who is selling raw chicken eggs with a hecksher? What company is paying for such a hecksher?
If some “dairy” company has a contract with a hecksher that all their products get the hecksher, the eggs frequently sold by that dairy company would technically get a hecksher, but the marginal cost of that hecksher would be de minimis (the fee for the hecksher would be on products that require supervision). Processed food such as powdered eggs need a hecksher but the discussion is over raw chicken eggs sold with unbroken shells.
Non-chicken eggs that occasionally get sold commercially, which is rare, are from kosher birds such as turkey and duck. Almost all eggs sold anywhere are from chickens, largely since chickens have been genetically modified to produce eggs roughly once a day and even when they are not fertilized.