Double Zero
I don't think your air race argument stacks up, and certainly doesn't add any weight to the case for AMRAAM - the reason the Harrier won was because the race involved the crews being in the city centres and the ac could be landed close to the start/finish points (hence the iconic shots of the GR1 at St Pancras station). The limitation for both GR1 and F4 on the oceanic stage was the AAR. The F4 beat the Harrier by a wide margin in terms of speed, combat radius, altitude and payload. And I don't think the F4 would be a suitable replacement either!