Mainly because it causes so much more pain at Heathrow. Sooooooo much hassle for so many passengers!
On that rationale alone, why not make visiting bigwigs use London Manston instead ? Would cause hassle for no passengers !
Alternatively, if (as it seems) the US Govt is finding money is a bit tight at the moment, land at Mildenhall, and by virtue of Obama being commander-in-chief of the USAF, the US won't have to pay any airport fees