They do not carry any more diseases than any other birds , few of the diseases that they carry are transmittable to humans and even those are very rarely transmitted. This is what the British Government vets said about the health risk the Trafalgar Square pigeons posed to the public:
"My Lords, advice from our veterinary team states that although diseases are carried by birds, those diseases are likely to be conveyed to human beings only when they are in prolonged contact with pigeons in enclosed spaces in the presence of dust from feathers or guano, and when eating food contaminated by pigeon droppings. None of those conditions applies in Trafalgar Square"
Pigeons are extraordinary birds.
Can it be a coincidence that of all the birds in existence it is the pigeon/dove that has been the chosen symbol of hope, love, purity, the Holy Spirit and also revered in Islam as the friend of the Prophet?