I don’t wash pots after boiling eggs or pasta. I just wipe them down with a wet paper towel (actually, that is just for the pasta since it occasionally sticks to the bottom, I don’t do anything to the egg pan unless one cracked). Everyone is way too germophobic these days. I guarantee you that the amount of fecal residue on a store-bought egg is less than the fecal matter you get in a Big Mac.
I don’t know why your eggs are cracking, but I find that if I put a small pinhole in the bottom of the egg (or top, I doubt it matters) before boiling, I get a perfectly boiled egg every time. No little indents on the bottom or top or anything. Because I put that hole in there, though, I wash the pan. Nothing comes out that I can see, but it’s really not that hard to clean the pot.
I personally don’t, but only because I make hard-boiled eggs for snacking, not to use in recipes. I don’t see the need to wash one pot that was used for boiling water, especially when there are no other dirty dishes to wash.
To me, it’s like washing out the measuring cup I used to measure water. At some point, it’s a pointless exercise and a waste of water, soap and time.
Robin
There is definitely residue left in the water from the eggshell, let’s put it this way, would you drink that water? I wouldn’t, though I’d happily drink water from a clean measuring cup. If the water isn’t clean enough to drink, the vessel should be washed, even if it’s just a quick rub and rinse.
To avoid eggs cracking when boiling eggs, I avoid boiling eggs. What I do instead is hard cook them. Bring the water to a boil, then remove the pan from the heat and put the eggs in it. Leave the eggs covered in the water for the appropriate time for the number of eggs.
After removing the eggs, of course, I wash the pan.