It's enough if North Korea (or Russia) allows China to use Korean airspace to send missiles and planes into Japan.
I don't think NK has enough conventional assets to do much damage to Japan. And NK is only going to try reunification if China is winning or China fights with them on the peninsula. They will need someone to protect them from US retaliation
Against the Anglos, you cannot show any hesitation or restraint, as that will only be interpreted as fear and weakness and invite aggression from.
If China only overflies NK, then it creates enough doubt for there to be a risk that SK might sleepwalk into the war without realising, or more likely, get dragged in by America without realising.
But PLA forces moving into NK in strength and attacking Japan from NK territory will make it impossible to deny that any SK involvement would lead to a join NK-Chinese ground invasion.
You also need to remember that America only has a token ground presence in SK. For America to be able to effectively contribute to a full on ground war against NK and China in Korea would require a massive sea based deployment of U.S. ground forces to SK. A deployment that would be basically impossible in the face of PLA air and missile attacks from mainland China and NK territory. Especially with massive missile and drone spam of the Japanese home islands and especially its port infrastructure facing Korea.
Distance matters, logistics matters. Overflying NK territory is vastly less efficient that being able to attack directly from NK territory. Overflying NK would also require the PLAAF long range strikers and tankers, who would be stretched as things are. Whereas direct deployment would utilise ground based missiles and bring shorter ranged fighters like the J10 into the mix.
Without the ability to sea lift massive amount of US ground forces and supplies, any ground war in Korea will only end one way.
In war, surprise and audacity are critically important assets, and if China can effectively use that, it can potentially force SK to sit out, even in a grey zone intel sharing fields, because of the overwhelming strategic disadvantage they will be trapped in, and the devastating consequences of being pulled into the war while so compromised.