Yes, washing them shortens the eggs "freshness time", but the Ga Dept of Agriculture stressed that in the class, that eggs being sold away from your home must be washed.
The egg is laid with a protective coating called "the Bloom". It keeps moisture in and air out of the egg. Once it is washed off, this barrier is gone and the egg starts to get older faster. As the egg loses moisture thru the shell, air is drawn in to replace the moisture.
When you wash fresh eggs for eating, the water temperature should be warmer than the egg.
For my personal eggs, I don't wash them. And, if someone comes to my house to pick up eggs, they can ask for unwashed eggs and no license is required. (If you sell the eggs away from your home, you need a license)