I have no idea what the USAF thought. But often--and particularly at that time--things got done as much because they could be as for any other reason. And then there is what my Dad said to sum up his Army service: "Son, there are three ways of doing anything: The right way, the wrong way, and the Army way."
I think the AIM-26A was the product of expedience and muddled, ex post facto requirements analysis than anything else. It was a design contradiction . Genie was a brute-force but logical solution to the problem of insuring the certain destruction of a dangerous, non-maneuvering, high-altitude target: an unguided, more or less ballistic weapon with a warhead lethal enough to make up for accuracy limitations in the aircraft fire control. Falcon pursued an opposing, more elegant logic: make up for accuracy limitations in the aircraft fire control and the limited lethality of a small conventional warhead with a guidance package capable of leading the missile to the target. As others have said, the latter approach proved unreliable, probably due to the electronics technology of the day and the relatively greater complexity of the solution. Seen in this light, the nuclear Falcon was an illogical design that managed to combine the worst features of these two opposed solutions: nuclear explosions over our Canadian neighbors' heads and unreliable guidance and control. So my guess is that the nuclear option was driven by doubts about the conventional Falcon's ability to get close enough to destroy high performance bombers and the need to rehabilitate (and preserve funding for) a USAF guided missile program.
We should also remember that the nuclear AIM-26A was cancelled, revived in 1959, and deployed in 1961. This was just as the U-2 program was showing Presidents Eisenhower and Kennedy that the Soviet Union did not have any significant, strategic bomber force, much less one capable of threatening the continental US. I expect that that revelation ended any serious interest in pursuing the complex, expensive, possibly dangerous, AIM-26A nuclear solution. The Genie was at least simple, although why we bothered with them once we knew that their designed targets did not exist is a mystery to me.
