They tried/are trying, but it's tough to be proficient in the 700 syllabi it requires to fly around at night these days and still maintain the currency requirements you need to go VERTREP for 7 months on USNS NON-TACTICAL.
Basically, we have ended up learning to play 160th at the expense of teaching JO's how to land on the boat, a mission that we actually do on a daily basis.
It's much bigger than just the training. Carrier Strike Groups have reluctantly allowed helos to be stationed ashore for prolonged periods.
If you are going to do NSW aviation correctly, then the unit needs to train and deploy with the SEALs, not just be available at Al Udied for 3 weeks.
HS has fought for many years to maintain CSAR/NSW shore dets in various theaters and have always received a lot of pushback. Once ashore, then the JFACC has as much control over you as the CSG/CVW does; the Navy does not like delegating control of its assets to other folks.
When the carrier depart the CVOA for port calls or to go to another AOR, then they will want to pull the dets back and take the helos with them. Once again, no continuity of support for the land based requirements of the SEALs.
Back in the 90's when there was a SEAL platoon on the carrier, then the HS squadron could train and deploy with them; that is no longer possible.
If the Navy is going to do it correctly, the need to dedicate a squadron(s) to the mission. Think of the air ambulance. HS-15 did that mission for 3 (I think) years. They were not tied to a carrier, so they were able to dedicate to that mission.
To provide dedicated support to NSW the helo squadrons need to be land based WITH the SEALS, not just in the same theater.
Once you go over the hurdle of dedicating them to the mission and land-basing them, the training is an easy thing to overcome.