Why new aircraft? Most such roles can be and are easily filled by refurbishing older aircraft that are on the market now; was B707, B737 and A310 for quite a while, currently it's the A330 and B747 (although the 747 is only used for VIP).
While existing aircraft can be retro-fitted to act as MRTT, MPA, AEW aircraft, the impression I had formed from the initial question was whether or not it would be worthwhile to use newer airframe designs which are more efficient and being newer, will have longer service lives.
When one considers the existing fleets of support aircraft and their respective ages, the question does have some merit. Take the Boeing 707 for instance, that airframe or derivatives of it have seen service as tankers, transports and a variety of electronic support aircraft, totaling nearly a thousand aircraft, all using a 1950's era airframe. As seen with the US KC-X programme, many of these aircraft need replacement almost immediately. Others (like the E-3 Sentry) still have some useful service life, but some thought likely should be given towards their replacement given that the newest examples are nearly two decades old now, as well as technological advances both in aircraft design as well as mission systems.
Again thinking of the KC-X programme, it seeks to replace the USAF fleet of KC-135 tankers with some new(er) tanker aircraft. The two contenders for it currently are tanker variants of the 767 and A330, airframes from the 70's and 80's respectively. In point of fact, Boeing's 767 line is currently expected to close if the current Boeing offer is not chosen as the tanker replacement.
IMO there are some rather obvious disadvantages to the current Boeing offer, in that apart from any manufacture for the tanker order, no new airframes are being constructed, therefore once the order is completed, the line closes and no additional orders for replacements, etc. At the same time, the basic Boeing 767 airframe is about three decades old, which means that improvements in design and efficiency are going to be minimal. Given that newer aircraft available and/or up-coming, it would seem more sensible to chose something newer, more efficient and still in production for civilian use.
As for the Boeing 737, it is currently the basis for the E737 Wedgetail/Peace Eagle, as well as the P-8 Poseidon MMA. My understanding is that the current iteration of the 737 dates from the 90's and while likely to be in production for some time, is going to be the last iteration.
One thing which peaked my interest as a possibility was the adaption of the Boeing 787, once it enters production/service, for electronic support duties. IIRC in addition to a generally more fuel efficient design and construction, one of the more notable features of the 787 is the amount of power the engines produce while in flight compared to earlier aircraft. The ability to generate significant power while flying efficiently, and the use of conformal arrays, paniers and fairings instead of a large rotodome like on the E-3 or E-767 would likely result in an aircraft that was more efficient to operate and maintain, as well as more capable per mission, than those currently in service.
Just something to think about anyway.
-Cheers