Titanic submersible es morte

The US has about 20 ships operating in the Mediterranean. It is definitely something the US could do, but it is not an operational priority for the US Navy. There are also legal issues surrounding such rescue operations and where you would put the survivors.
It also likely involves entering the territorial waters of other countries to even perform rescue operations. IIRC, US military vessels are sovereign US territory so picking up survivors becomes problematic if the survivors ask for asylum or claim refugee status.