Because it worked so well back in 1940 with Japan.
Aggressive military dictatorships aren't always deterred by anything less than war. Can you think of a measure less than war that would have deterred Japan from its path of conquest in Asia and war against America? Surrender doesn't count.
. . . amid all their paranoia and psychopathy they are honestly scared about what happens to non-nuclear countries once USA tells them "you are not my friend" and how different it is when the one at the receiving end is an ICBM-capable country.
Your theory needs some adjustments. North Korea was at war with South Korea, the UN powers, and through that the US before there were ICBMs. You're trying to paint a 60 year old war with a 10 year old brush and it doesn't work. Many countries have had an interest in nuclear arms and many of them were US allies. I don't think your idea holds water. North Korea wants nuclear weapons for the power, not just to use against the US.
By the way, did you take any notice of what happened to the "friends" of the USSR that went off script? East Germany? Hungary? Czechoslovakia? Afghanistan? I don't recall the US invading a friendly nation like that.