> It's secondary radar so it only sees planes with a transponder, but that's usually all of them.

In particular we're talking here about aeroplanes on an approach to a major airport (if they aren't on approach then by definition they aren't choosing between ILS and a visual clearance, and if it isn't a major airport why are we trying to bunch them up more?).

All US major airports have a "Mode C veil" which means there's a regulation requiring aircraft near those airports to have transponders ("Mode C" is a transponder mode in which the aircraft reports its own assessment of its altitude based on air pressure as well as a four octal identifier).