Oh, you don't know the half of what I've kept in the house before... in my "past life" I had about forty house birds of a dozen species that were mostly maintained free-flight in one specialized room of the house that I basically made into the "indoor aviary". And for a few years, I had a garden enclosure where they summered. Two or three pigeons is *nothing* compared to what I used to keep up with!
Keeping that room spotless, now that was a bit... messy lol. But also a lot of fun! I sold most of the flock when I moved and was unable to have many pets for a few years. I used to raise cockatiels, finches, canaries, and budgies. I fostered a pair of ringneck doves for a few months and kept one of their chicks for a few years.
Birds are messy pets but if you keep up with it (and I am a bit obsessive about cleaning anyway) they are not bad as far as I am concerned. I use air purifiers to catch dander, dust everything weekly, scrub cages every couple days and vacuum the house top to bottom every morning.
I just view it as... life is short. Birds make me happy! They're worth a bit of cleaning. I wouldn't recommend this many to anyone who doesn't want to make a hobby out of it because it is a big commitment but I really enjoy it.
I was contemplating I could very easily set up an enclosure out of a dog cage like this (this one is not my picture) for Rosie and if I got her a companion in a quieter part of the house. It would not be really much more mess than I manage as is with the two pigeons and the three cages housing smaller birds.