> The "shrapnel" would consist of lightweight scraps of carbon fibre and sheet metal
I suspect that people who are concerned about shooting down planes over London are worried less by the debris of the missile, and more by that of the target.
Not in TFA, which is about the possibility of AA-missile shots deliberately provoked by a harmless dummy.
In the scenario of an attack by something that is actually dangerous, shooting it down will almost certainly cause less damage than letting it hit its intended target (at least when the target is a mass of spectators at a sports event).
I suspect that people who are concerned about shooting down planes over London are worried less by the debris of the missile, and more by that of the target.