I recall reading that these two missiles have onboard radar for mid and late course correction, but I never read any suggestion the firing plane doesn't need its own radar for target selection and initial guidance. Yet here, the various fighters using them can leave off their radar, still fire, and have the enormous advantage of never giving their position away by emitting signals.

 

Still more oddly, I am prompted to turn on my radar when a plane comes within range, but I can choose not to, and the missile performance doesn't seem any the worse for not having the plane's radar on.

Yeah, that is the great advantage in air-to-air combat of a Active Radar Homing missile as AIM-120 AMRAAM in face of a Semi-active Radar Homing missile, as AIM-7 Sparrow

I recall reading that these two missiles have onboard radar for mid and late course correction, but I never read any suggestion the firing plane doesn't need its own radar for target selection and initial guidance. Yet here, the various fighters using them can leave off their radar, still fire, and have the enormous advantage of never giving their position away by emitting signals. Still more oddly, I am prompted to turn on my radar when a plane comes within range, but I can choose not to, and the missile performance doesn't seem any the worse for not having the plane's radar on.

Its just the simplicity of the model coming through, again. Take the AIM-54 Phoenix, for example. In real life, the Tomcat's AWG-9 radar is used to illuminate targets, and provide semi-active guidance during the missile's cruise phase. The missile's own seeker does not come into play until the terminal phase of the engagement, or at very short ranges. Because there is a terminal active radar seeker, HCE doesn't penalize you by insisting that you energize the F-14's radar. Neither does it limit you to shooting only six missiles at six separate targets (if the Tomcat could carry more than six).

Don't worry, reality is catching up to the model though... Offboard cueing for everything!