The USN's overall, strategic goal is to keep the hostile waters in someone
else's back yard via force projection.
More advanced and quieter nuke propulsion? Sure. They'll look into it.
More advancements in patrol capability (the P8 Poseidon for example)? Defiantly, but think about where most of these US patrol aircraft work (hint, it isn't near our continent).
Diesels (and by extension, AIP) haven't been a US priority since the 1980's and that was mostly due to heritage and basing concerns*. The Navy got over diesel boats a long time ago.
As a former crew member on the USS Barbel (SS 580), trust me, they ain't coming back.
*- Japan had a prohibition against nuclear powered boats being based at their ports
at the time. That has since changed.