> Why does the escort survive the mother ship?

Why not?

The function to escort is to give AA or ASW coverage to whoever rents it.
Once you are sunk, the contract has ended, ceasing to be useful to you and it does not have to give coverage to those who have not hires  it or roam like a ghost ship shooting at everithing in its path.
It is not fair that everithing you have strugged to survive, sinking or escaping from attacks by dd, cl, bb, bombers, TB,..., I threw on the ground a "robot" that no longer contributes anything to who rented it.
Just yesterday  see how one of this "survivers or robot" sank a DD and a CL taht had skillfully survived the head of the battle with oder DD, CL, SS or even som BB, and this, apart for being desperate, is truly unfair when you have beaten with other biggest or strongest players, let a robot sink you.
If you asking you to understand my position as ss driver but as a player.That if you are able to have empathy.

Escorts being so good at ASW and AA is a problem. The fact that they don't just basically disappear when their parent is sunk is not.

In my opinion escorts should not exist at all. If you want to shoot down planes or sink subs, do it yourself.