Is there a reason why this could this not be brought under control naturally by providing habitat for predator species, like hawks or eagles? Apparently Peregri

Is there a reason why this could this not be brought under control naturally by providing habitat for predator species, like hawks or eagles? Apparently Peregrine falcons have done quite well in urban environments [1] [1] https://www.telegraph.co.uk/news/earth/earthnews/3324408/Peregrine-falcon-adapting-to-urban-lifestyle.html https://www.telegraph.co.uk/news/earth/earthnews/3324408/Per...