No falconer in his or her right mind flies at pigeons in the UK - there are so many of them that it is about the quickest way to lose a bird. Geese are too large to be flown at consistently with safety. Rabbits will not be scared away by raptors as they are hunted by them so often in the wild. Although they can be caught by raptors fairly easily, it is a time consuming and therefore expensive way of controlling them. Note that the healthier the rabbit population in the wild, the healthier the wild buzzard population, so wild buzzards hunting daily fail to bring the numbers down.
Gulls are usually too numerous and are very aggressive with birds of prey.
Many Gulls are protected species and falcons will not differentiate between those that are and those that aren't. Any species other than those legally termed as vermin have the same hunting laws and seasons applied to them as regards hunting with birds of prey, as hunting with guns. Many species are of course protected by law and should they be caught persistently while using birds of prey for 'bird scaring' this could well lead to prosecution. If there are other species of birds within sight of an area to be cleared, such as domestic fowl or protected species of birds, they could well be caught by a ranging falcon. Our falcons, when hunting can be anything up to a mile away while in the air.