It strikes me that the Navy could build an extendible shaft into an extension on the back of every submarine conning tower, then give this the end of this shaft a multi-axis docking collar. Then when a sub goes down, another sub of the same class (and thus crush depth) could come to its rescue within a matter hours or at most a couple/ of days. No need for limited-capability specialized equipment.

I can see three reasons why the Navy might not want to go that route:

1) Expense - The cost of designing, building and installing such shaft/collars across the submarine fleet would be very high. But is it more than what would it cost to replace an entire trained submarine crew or two?

2) Difficult of Installation - Retrofitting something like this to an existing pressure hull would be a very ticklish business. But installing one in a new-built sub should be much less difficult.

3) Classified Crush Depths - Actually using the installation to rescue a sub would necessarily reveal how deep a sub could go before hull failure (since Everybody And His Cousin would send vessels into the area - which would necessarily be in international waters - to monitor the operation). Just abandoning the crew to their fate might be seen as a better course than revealing this information.

I suspect that this last consideration - classified crush depths - may be the reason that the current rescue equipment can only operate in relatively shallow water. After all, if we can build an entire enormous sub that can go X deep, why should we be unable to build a small rescue submersible that can get down to that same level? Particularly since the submersible need not be streamlined for high-speed travel and can thus have a spherical hull (rather than a structurally-weaker elongated one).