Because it costs money to keep an airfield open for large aircraft operations eg taxiways have to be repaired and kept FOD clear.
There are many parts to the jigsaw, some of which prevent large aircraft movements from taking place at smaller airfields despite the user unit wanting it
Movements teams, ac handling equipment for loading/unloading pallets, pax processing, catering, customs, crew duty outbound (pre-positioning ac to load at start of 14hr day) and inbound (use of aircraft the following day, in the event of a delay).
I am not saying that they are not achievable, just that with the very limited manpower and assets we have these days spread so thinly, keeping your aircraft operations from one large base does make sense, espeically when the C-17 (or other large ac) movement isn't the only one going on.
In my previous job there was a suggestion to reduce the length of the runway to 3000ft as this was all the Apache needed thereby reducing costs at Wattisham. Fortunately this was thrown out!