I love the idea of having a dovecote, but I can't see it happening any time soon. Here are a few titbits of info.
Pigeons feed on crops. They don't differentiate between the farmers fields or a small vegetable garden. They can eat a fresh planting of beans down to the ground in hours. In this area pigeons are a major pest and huge flocks of them can descend and obliterate a large portion of a crop in hours. Farmers shoot them, or allow hunters to use their land.
The dung was definitely used for fertiliser, but they were not "broken open" - they usually had a small door and access into the central space. In the central space you could reach into any of the nest holes. Thus the farmer could harvest the squabs directly from the nest before fledging, and easily collect dung.
A baby pigeon that is about to fledge for the first time is known a "squab"- they actually LOSE weight once they start flying, and have most meat on them at this stage.
Pigeons mate for life. The keeper can control this to some extent by closing them up together until they have bonded, and allowing only one or other to fly at a time. Many dovecot designs have doors hatches that can be opened and closed from floor level using strings.
I'm not sure that the benefits of having a dovecote outweigh the potential harms they cause to local crops.
Moderator, Treatment Free Beekeepers group on Facebook.