If I may over simplify the complex situation a little — South Korea’s President Moon Jae-In is a politician from the left. A quarrel with Japan improves his street credibility with his leftist supporters; so I can see how his Minjoo Party of Korea benefits from this tension. The Minjoo Party of Korea supports an appeasement policy toward North Korea
(= Sunshine Policy), and there is a bit of a left-wing nationalist
inclination. See this KEIA pdf article
to set the scene. South Korean politics faces lots of blaming, renaming, claiming, laming, gaming, "same-ing," but not taming — which is bottom feeding politics. Bottom feeding (or win-lose politics) is fine for a domestic audience but the Koreans need to learn to dial down the hate Japan rhetoric as part of their national identity, at the right time — to have a functioning state to state relationship with Japan, if they are to take the North Korean threat seriously. Below is a list of North Korean missile launches in late July to mid-Aug 2019 and a video to set the context:
Jul 25: KN-23 / Hodo peninsula
Jul 30: MLRS / Wonsan
Aug 2: MLRS / Kumya county, South Hamgyong province
Aug 6: KN-23 / Kwail county, South Hwanghae province
Aug 10: SRBM / Hamhung
Aug 16: (?) / Tongchon county, Kangwon province
Instead of concern with the hostile North Korean behaviour, President Moon, from the Minjoo Party of Korea are successful at demanding a response from Japan. They got what they wanted — a Japanese response that demonstrates the harm the Koreans can do to themselves by promoting hate in their form of nationalism.
To better understand choices, please note 2 additional criteria on diplomacy and its effective conduct. One, if Korea-Japan diplomacy is consistently experiencing "one step forward/two steps backward," then the policy must be acknowledged as failing and in need of adjustment. Two, diplomats must be pragmatic and satisfice rather than optimize. By these 2 criteria, it is fair to say that South Korea-Japan diplomacy is an utter failure. Each side is seeking maximalist goals with an unwillingness to compromise. South Korea's decision to renege on the 2015 comfort women agreement; the court's ruling on Japanese businesses compensating Korean workers; Japan's delisting of South Korea from the export whitelist; and South Korea's retaliatory de-listing on have taken relations not one step backward but five steps backward. As CSIS has noted (see link below), the US should appoint a special envoy who would call on Japan to engage with South Koreans and who would discourage Seoul from more public maximalists statements like "We will not lose to Japan again," which leaves no room for compromise. Now the Koreans need to learn how to climb down from their position and transition to a working bilateral relationship with an ally.
CFR has a backgrounder: What's the Status of North Korea's Nuclear Program?
Perhaps the US absence is the only way to actually get these two players to resolve things once and for all. IIRC, it isn’t just WW2 claims but also for stuff going all the way back to the first decade of the 20th century.
Not only are Japanese interests hurt in the Korean-Japan storm in a tea cup, American interests are also being hurt. While Trump may not care or understand the issues and dispute, the US Foreign Policy establishment will use this incident to judge how reliable Korea is a partner for the Americans going forward — which has geo-political implications. See this CSIS article: Finding a Way Out from the Japan-Korea Crisis
Differences between Seoul and Tokyo over the North Korea problem have only deepened. Japan’s interests rarely overlap with South Korea’s when it comes to negotiating denuclearization. Similarly, Korea’s President Moon’s desire to relax sanctions on Pyongyang to move negotiations forward runs counter to Abe’s insistence on maintaining an international coalition to force Kim Jong-un to end his nuclear program. Tokyo has worked hard to persuade a coalition of UN members to support sanctions and work to ensure they are complied with. The United Kingdom, France, Australia, and Canada have all worked with Japan to monitor sanctions implementation through maritime patrols and surveillance. For Tokyo, abandoning this hard won international coalition would be tantamount to giving up on the UN’s role in international security—a premise of multilateral cooperation that is a pillar of Japan’s own national strategy. Seoul and Tokyo want different things from Washington when it comes to negotiating with North Korea. The larger difference that shapes Seoul and Tokyo’s relationship, however, is over China. On the surface, it might seem that both nations would want to double down on deterrence and on their alliances with the US. And yet each sees the other as amplifying each other’s vulnerabilities in their long-term ability to manage China. See: Seoul and Tokyo: No Longer on the Same Side
When Seoul and Beijing join in their criticism of Tokyo’s prewar behavior, it grates deeply in Japan.
Everybody in the Indo-Pacific is hedging with the rise of China. With Trump’s unpredictability, there is strong incentive for Japan and Australia, as G20 members, to grow closer bilateral defence and economic ties (see: Japan – Australia Summit Meeting
)— this long term bi-partisan development in Australia. Strategic hedging intersects with defensive realist precepts in that balancing against a potential threat, conducting a restrained policy and to boost defence capabilities to enhance security. The shared aim is to avoid the repercussions of a security dilemma situation. Hedging strategies enable bandwagoning including economic and or socio-political cooperation with the threatening power to try to side-step future conflict with it. Likewise Australia, Indonesia and ASEAN have enhanced military and economic ties and have grown closer (see: Australia-Indonesia Relations: Strategic Partners in a Time of Change - AIIA
and Reinforcing Indonesia–Australia defence relations: The case for maritime recalibration
)— again a long term trend despite the differences.
Where is Korea as a G-20 member and it’s geo-strategic thinking? The CSIS article is damming on Korea’s lack strategic thinking and it’s inability to engage in strategic hedging. If no external party in the G-20, including the Americans, know how to work with the Koreans, how can the Korean work with others in Asia and Oceania to address their concerns about North Korea?