Short answer
Do not automatically wash eggs using an improvised household method. Whether washing is appropriate depends on local regulation, how the egg will be stored and whether the process controls water temperature and sanitation.
The shell has a protective surface
A thin cuticle helps block pores after laying. Abrasive or poorly controlled washing can damage that layer, spread contamination over the shell or encourage movement through pores. A visibly clean nest egg needs less intervention than a dirty one.
Commercial washing is different
In countries where eggs are washed commercially, processors control water temperature, detergent, sanitiser and drying. Rinsing under a household tap is not the same process. Washed eggs should enter and remain in the cold chain.
Start with flock and nest hygiene
Clean nest boxes, frequent collection and rejecting cracked or heavily soiled eggs reduce the need for washing. Follow the advice of the relevant agriculture and food-safety authority, especially if eggs will be sold rather than used at home.