You don't build ship type A because a neighbour is building ship type A. That's just dick-waving. You build it because you have a use for it. An LPD is for amphibious operations. It doesn't fight LPHs.The draw back on those JMSDF ships is that they have no hangars. Why? So other can't call them aircraft carriers. But things are changing.
It is wise for S. Korea to build the LPX type ship. Because the JMSDF will in about two years time have an LPH...
Also, the 16DDH isn't an LPH. It lacks facilities for carrying troops, vehicles, etc., isn't equipped to load & unload vehicles, can't carry any landing craft, or even Mexeflotes, & doesn't have the access ways for fast disembarkation of troops. It has fine lines & big engines, which reduce internal space (amphibious ships are carefully designed to maximise internal space). In other words, it isn't equipped for amphibious warfare.
But it is equipped to lead an open ocean antisubmarine flotilla, especially when one considers that Japan has some frigates & destroyers with helicopter landing pads but no hangars. 16DDH has a command suite, & hangarage & support facilities for several helicopters. It's fast: it can keep up with destroyers & frigates. It could support sustained helicopter operations in the open ocean from a few smaller ships which without it would only be able to support helicopters for short periods, or with shore support. It has sufficient missiles to put up a decent defence against air attack (with a Kongou along, a bloody good defence). The name is wrong: it's really a helicopter cruiser, or helicopter carrier, not a "destroyer". But it is primarily an ASW ship, & designed to complement existing JMSDF ASW ships & enhance their capabilities.