To simplify the issue, compare the late model Sparrows, AIM-9M against their ARH counterparts(AIM-120).
The AIM-120 offers BOTH a "semi" SARH and ARH mode of launch.
The AIM-7 is limited completely to SARH.

It's easy to think the SARH gives you a "second chance." That's not true. Once the first missile has gone wild, you may as well take another missile shot.

That said, there IS an advantage to SARH, mostly against ground clutter where if you're operating a high power radar like that on a 14 or 15, you can really light up your target. Even in semi SARH, you'll let the missile get close enough that power limitations don't matter. Other than that, in typical BVR engagements, SARH is only a liability.