SSKs or SSPs have no place in U.S. doctrine. Our Navy is constructed around blue water maritime superiority.
SSKs are primarily for coastal / strait defense. They worked for Germany in WWII because their coast is the size of the coast of Texas bordering the Gulf of Mexico America. Using SSKs or SSPs to defend the U.S. coast would require accurately predicting exactly where a fleet would attack along over 28,000nm. So more likely than not, they're out of the fight and can't do anything to get there.
On top of that, any force that comes to U.S. shores will be facing a ton of homeland coastal defense assets that are far superior than anything an SSK can do to defeat the enemy forces.
And it's not like we can't use SSNs in such a scenario.
SSKs worked for us in WWII because the Japanese couldn't figure out ASW, and because ships moved slow enough to be able to get our SSKs into position. With modern merchants going 20+ knots and warships going 30+ knots, they'd be of limited effectiveness. Plus we've had advancements in sensors that can pick up snorkeling submarines from really far away. I can't see how you'd get an SSK into a place like the SCS or ECS in time of conflict and have it come out alive.
For SSKs to be remotely valuable, we'd have to be facing an adversary who can mass an amphibious invasion force that includes the capability to establish localized blue water and air superiority over anything we can throw at it, including SSNs.