No one is talking about a satellite guided surface to air missile system.

We outlawed sticks because sticks can be used to press the red "do not press" button

Congratulations, we’ve mapped the space of possible harm from mild discomfort to death.

What's the idea behind a satellite guided surface to air missile system? The ground station detects the target with radar, derives a set of GPS coordinates for an intercept, transmits those coordinates to the missile, and the missile guides itself to them via GPS receiver? Seems suboptimal.

Something like that. It’s really only useful when you have to intercept at really long distances, as in ballistic missile defense.