Harry Hillaker (Mr F-16) once remarked that the natural evolution of a fighter was in terms of greater zero-fuel weight (payload and equipment), which meant more thrust and more fuel to maintain performance. Eventually, he added, you would run out of wing area and external stores capability, and if you ever saw anything above the wing you knew the limit had been reached.
The F-16 had two volume-adding mods in its lifetime: the conformal tanks (the first set had been designed in the 70s) and the originally-Israeli fat spine, which was intended to create a two-seater with similar internal fuel to the single-seater.
I don't think it would be a bad idea, in fact, to design conformals into a fighter from the outset. It would be a nice way to add flexibility and it might be possible (if difficult) to add them in a way that minimized LO issues.
I too tend to be skeptical about the idea of conformals reducing drag, except when qualified by "with the same fuel load" or even "loaded for equal range". However, ISTR being told in one case that the jet trimmed better at subsonic speed with the conformals in use.
Finally - looking at the F-35, I have no idea where you'd put conformal tankage, except maybe on the upper rear centerline. You could put a few gallons into the horrible wart that covers the Noggies' brake chute, even. And IMHO the A/B versions are already at their limit for wing loading.