They don't jump at the exit speed Cooper had.
And they jump with a static line. No need to stabilize and pull a ripcord.
and pretty sure they don't jump with the tether loose
You can look at pictures. The one's I've seen, all the gear is attached to body well, at exit.
They can be pretty heavily loaded up.
Cooper wasn't heavily loaded. No reason to get weight off his body at ground impact.
Any tethering is most likely for that reason..and released post exit...not to "detect ground"
That seems silly.
377 can comment.
All I know is that this is how the military jumps with a lot of equipment.