The Genie was a product of the early 1950s, with development beginning in 1951 and the missile operational by 1956. The original idea was to counter formations of Tu-4 Bulls (the reverse-engineered B-29s in Soviet service), and I'm sure bombers in tight formations were on their mind. But, even if they weren't, with guided missile technology in its infancy and not ready for deployment yet, machine guns inadaquate to shoot down more advanced bombers, and the unguided "Mighty Mouse" rocket clusters not offering much chance of really taking down a bomber either, the idea of using waves of Genie missiles against incoming bombers seemed the most viable method of shooting them down at the time.
Sometimes, there are no real answers. I don't think the Genie concept was ever particularly workable as an operational concept and they never even bothered with a live test engagement. The only test detonation of a Genie was the publicity shot. I'd say that a gun interception with a swept-wing jet interceptor should have been viable*, albeit dangerous as hell since the Tu-4 swapped out the B-29's .50s for 23mm cannon one-for-one. It's the Tu-16 on a one-way trip or a Tu-95 that fighters would be hard-pressed to catch, but they'd be hard-pressed to get a Genie within launch parameters too. Not only does it have to be within 2.25 MOA dispersion, but the timing on the fuse would have to be within about half a second in order to not overshoot or undershoot the target (~900 m/s) assuming the target didn't react at all.
2.25 MOA isn't remotely practical with aircraft guns even now, let alone a giant folding fin rocket in the 50s. Nuclear security theatre maybe. I don't think a serious air defence system would be deploying AIM-4 Falcon missiles all the way into the 80s (Falcon/Genie was the weapons fit for both the Canadian CF-101 Voodoos and USAF F-106s in NORAD)
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