I once found pigeon nest behind my window with 3 eggs in it. I didn't have the heart to destroy the nest. Little did I know about what filth I will have to clean up once they take off. Also, they left behind some very tiny beetles that I battled with for few weeks to come. They were so tiny they managed to squeeze in through the window's sealing.
Surprisingly little excrement before hatching, compared to what comes after. And even that is less ugly than what happens when the magpie gets the chick before it gets too big. My current approach is allowing them to breed but sterilizing the eggs with a quick round of cooking. I feel sorry for them when they are close to giving up (how much conflict between hope and growing doubt fits into a pigeon head?), but just removing the eggs will lead to a another attempt and sometimes I'm away for long enough to allow them to get from zero to hatching
(that's how I learned about the magpie situation, was away long enough to have an entire laying-hatching sequence after leaving when freshly sterilized, I suspect they gave up early, magpie discovered and took the abandoned eggs, remembered the spot and came back to the chicks after the next breeding attempt - pure speculation but the schedule would just fit my absence)
This year I found an egg again. I threw it away.