Moths? You gotta absolutely eradicate the fuck out of these before they destroy your clothing or your food.
Rats, well, you don't want them in residential areas [1], and you don't want their feces around food preparation areas like kitchen.
Pigeons, especially their poop, are a massive danger for historic buildings [2] - their poop, similar to acid rain in the 80s/90s, is acidic and erodes the substance. In addition, it is extremely nasty to clean up, you need to wear a full PPE suit - our OSHA equivalent has a dedicated guideline just how to protect yourself while cleaning up pigeon poop [3].
[1] https://www.independent.co.uk/news/world/americas/crime/indi...
[2] https://www.kath.ch/medienspiegel/taubenkot-gefaehrdet-bausu...
[3] https://www.bgbau-medien.de/handlungshilfen_gb/daten/pdf/201...