We all agree that Sparrow was a high altitude bomber killer.
Wasn‘t Limited War supposed to have gotten higher priority under Kennedy/McNamara?
I don’t know of any new, more maneuverable air to air missile project started until ~1969.
Were they hoping a Limited War enemy would be flying TU-16s/22s?
The problem is that until your missiles actually meet the enemy's airplanes, there's no telling how well they will actually perform. Sure, Sidewinder was proven by the Taiwanese in 1958, but IIRC there was an element of surprise there, and both the launch platforms and their targets in that fight still belong properly to the classical dogfight era; they are the last gasp of the fighter philosophy which arose out of WW2. You can talk about being prepared to fight conventional wars all you like, but until you actually engage in the fight with planes that aren't dogfight-optimized and are suddenly, abruptly restricted by ROE, and find the current missiles don't work within those constraints, there's no perceived NEED for any new project.
You also can't really live fire developmental products against threat representative targets, at least not at that time. Modern target drones make this more doable, but its still a challenge.
Also it has become clear that the Sparrow team did everything they could, but a lot of the missile's shortcomings in the early days of Vietnam were due to HMI issues. There was no clear indication that a target was in the missile's relatively tiny No-Escape Zone, or even in a good position for a shot. They had range, respective velocities, and other tools to estimate it, but the fire control computers controlling today's AAMs do unbelievable amounts of work to give a pilot a simple and accurate idea of how likely they are to achieve a kill if the missile is fired at that point.
@pathology_doc Unfortunately no ideas, everything I've seen about AIM-7R is locked up, so to speak.
