There's loads wrong with this, notably that Trump had no problem either with the concept of dynastic succession or the brutality, purges, and executions that have accompanied the young Kim's ascent to the throne. But let's leave that as a pop-up footnote for the moment.
Though given their respective temperaments, I wouldn't be surprised if they got along swimmingly.
There are in fact good reasons why not, of course. Most notably, it's completely unacceptable to resolve Korean peninsular issues without actively involving Seoul. However, North Korea has always claimed that its nuclear weapons program is a deterrent against the nuclear arsenal of the United States, so if they insist it's a bilateral issue, why not take them up on it and see what happens? We've seen where the alternative leads.
When Barack Obama was running for president in 2007, he said he would be open to meeting without preconditions with the Iranian leadership to resolve the nuclear standoff. Hillary Clinton, his rival for the Democratic nomination, pounced. Obama could not be taken seriously as a candidate for such a stance, she said. Obama's statement was painted as a huge, potentially campaign-ending gaffe.
Except the American public didn't really care. Obama won the nomination and the presidency, and while he never did have a sit-down with Ayatollah Khamenei or any Iranian president, he did oversee negotiations of the Iranian nuclear deal that, even in the era of Trump, so far appears to be holding. Crisis averted.
This week, Donald Trump said he would be "honored" to meet with North Korean leader Kim Jong Un, called him a "smart cookie," and credited him with leadership skills for having taken over his country at such a young age. He had said something similar in 2016 on the campaign trail, and the comment fits into his longstanding worldview that if he can just meet face-to-face with important people, he and he alone can work out a deal.
Media and establishment types erupted on Twitter. And yes, there was the predictable partisan hypocrisy: conservative media and leaders let the comment go where they would have pilloried Obama as weak and naïve for having said the same. But does the general public care?
The real problem here is the question of legitimacy. The establishment foreign policy worldview is that meeting with bad leaders grants them legitimacy, as if even acknowledging them is the equivalent of Chamberlain capitulating at Munich. This is frankly silly, akin to the game kids play when they annoy a child by pretending he or she doesn't exist.
US: North Korea doesn't exist.
North Korea: I exist!
US: Did someone just say something?
North Korea: (Launches rockets)
This isn't just an American tactic, though we do it more often than most. Long ago, the North Koreans decided that the South Korean government was a puppet state and demanded direct negotiations with the United States to end the Korean War (which is technically ongoing, if frozen). This posture is equally unreasonable, and the United States has insisted on dealing with the issue of denuclearization on the Korean peninsula through negotiations with six parties. The North keeps walking away from these talks and, in the meantime, advancing its nuclear weapons and missile programs.
The fact is, regimes gain legitimacy by their existence and their ability to govern and hold territory, regardless of how reprehensibly they do it. It doesn't matter whether Washington considers Pyongyang's government legitimate. It's there. Nor is it likely going away anytime soon, and certainly not due to any (sane) action Washington can take. Why not engage it by any diplomatic means available?
Now, do I think Trump and Kim Jong Un can resolve the Korean War with a face-to-face? Of course not! But why not give it a shot? Nothing else has worked, and this latest posture from Trump is a hell of a lot better than the previous week's threat to pointlessly and destructively turn the frozen conflict into a hot one with hundreds of thousands of needless casualties. Too often in international affairs, even the willingness to negotiate is denigrated as weakness. The only thing this stance does is allow problems to fester. Let Trump and Kim meet if they want. Why not?