Because LGW is so busy. All these a/c want is a couple of tons of fuel and a quick departure, neither of which would happen as quickly at LGW than at LTN. Even if it if it was a tech problem it would probably be easier to bus people from there than LGW anyway (and theres no BA airbus engineers at LGW in any case).
As to turning up with less than minimum fuel, as mentioned we dont - we aim to arrive with the CAA's legal amounts. Carrying any more without reason (and theres plenty of those!!) is a waste & harmful to the environment
Its rare that Ive carried any extra - and Ive never diverted yet in 400+ arrivals.