It wouldn’t surprise me at all if early heat seeking missiles used just a PID controller, since a big part of what makes PID attractive is the ability to implement it with electrical components. Take a pair of IR photodiodes and wire them such that their difference is the error of your PID control, wire the output of the PID to the steering on your missile, and suddenly you have a missile that points at the nearest IR target (on one axis of course).

Modern missiles do better than this, but a missile wired this way with a proximity fuse would hit the target a reasonable amount of the time. Not silly at all if you haven’t invented microcontrollers yet.