The Airport Madness does have an overshoot button but you don't control it then!
But in real life you do! In the game you can't, and then a middair can happen.
I never thought of the overshoot... it doesn't really have an option for that... unless you cancel the approach and issue headings and altitudes
That's how it's done. Not often required in the game; you just slow the following down. Required occasionally in real life, if there is too big a catch-up.