If you believe that the payload was a sophisticated signals investigation platform, sending a radar-homing missile towards it potentially gives your adversary access to information about your missile's capabilities.
I guess. Likely the F-22 radar itself is a better kept secret than the AMRAAM which has existed for a long time and in semi-recent versions in places like Pakistan. So that could be a reason: firing a radar homing missile requires using the plane radar (?) and you'd prefer to avoid that if possible.
