Whether the missile has a solid fuel motor or not isn’t the point. In many cases, the missile has a boost motor to get it off the launcher and rapidly accelerate the missile. This motor will burn out and a sustain motor will continue to power the missile. Eventually, this motor will also burn out. The missile will continue to fly and can be further guided to the target.
The point is this. If the missile sustain motor burns out significantly below 13,000 feet, then no one saw a streak fly all the way up to the 747.
Any incremental increase in lethality due to unburned propellant is not likely to be significant. I don’t know of any air defense system that has a design requirement for unburned propellant at intercept.
That's not how the missile works unless the target is stationary. Once the motor burns out drag takes over and without thrust the missile head either explodes (if designed to do so) or the missile falls back to earth. Once the missile burns out it falls back to earth on a ballistic trajectory. The fins on the missile are used to maneuver the missile while thrusting. They are not wings. Once the missile burns out it no longer has lift.