To me it is clear that for quick and reactive heavy lift, the C-17 is the natural proven platform of choice.
My concern is that for realisation of aid relief strategy, you require the assets to distribute aid once in theatre, and for that SH and C-130 aircraft are your friends.
Don't know about that last statement. C-17s can get into just about any airfield a C-130 can get into, while delivering more than 4 times the relief supplies. And a really small airfield is often a poor choice for delivering supplies. How so? Small airfields are also austere airfields and without security forces in place, the aircraft could get overrun by desperate locals. Achieving and maintaining security is a huge deal in such an operation.