Why would japan need carriers?
Its one thing to be able to tap into logistical, development and operational with the USN and its carriers. Guam is nearby and a huge base, US carriers are always nearby Japan. Being able to train, operate with, use the weapons of, share parts with USN aircraft is always going to be positive for both parties. If Japan is short a few parts or the USN is, a shared logistics would benifit both nations. SH has the ability to network in with other SH providing a huge capability benifit when operating with the USN.
Thats completely different to Japan building its own CTOL carrier and operating a fleet of hornets off it. Said carrier would have to be 40,000t+ and I don't see japan building a target that big. Wheres it going to go? China? North Korea?
SH would also offer growler capability to the japanese. Something that may be very important in their region against certain nations. There is currently no other aircraft that offers that kind of capability.
That said, another big hornet user is also Australia which japan has strengthening defence relations with. It would also allow joint training and operations together, possibly overseas deployments. If war was to break out, Japanese fighters could operate out of Australia or Australian fighters operate out of Japan.
Japan could buy 48 SH. Place orders for F-35's once the F-35 come on line, continue to use the SH for strike etc with a few growlers. Essentially the SH becomes the low while the 35 becomes the high.
By the time the F-35 order is filled the SH are starting to retire off. Those F-4's aren't going to fly for ever (first flew in the 1950s!!).