Source?

The operating depth of most submarines is ~300 -- 500m (980 -- 1640 ft), roughly one-third to one-half the depth you cite.

The two USN nuclear submarines lost due to pressure-hull failures, the Thresher (1963) and Scorpion (1968) both failed at depths of 1,200 to 2,000 ft. Threser's test depth was 1,300 ft (400m), and she was operating at about this depth when communications were lost. Scorpion likely failed at 1,530 ft. (470m).

<https://en.wikipedia.org/wiki/USS_Thresher_(SSN-593)#Cause>

<https://en.wikipedia.org/wiki/USS_Scorpion_(SSN-589)#Disappe...>

There are other submersible vessels in the US Navy which can and have operated at greater depths, notably the submersible Alvin and bathyscaphe Trieste II, but those are not combat vessels. Alvin's test deopth is 6,500m (21,300 ft). Triest II's predecessor, Trieste, reached the floor of the Challenger Deep in the Marianas Trench, deepest known spot in the oceans, at 10,916m (35,814 ft). Trieste II incorporated the pressure sphere from its predecessor.

A more conventional, but still experimental, submarine, the USS Dophine (AGSS-555) was a deisel-electric research submarine which reached a depth in excess of 3,000 ft (910 m), probably in 1969. The boat was in-service through 2006.