Hi--wordy response, interesting subject. Thanks.
tl;dr answer is "Eh, its not so simple." but you're right on a basic level.
No, the North Korean ballistic missiles have from my non-classified top-of-the-head understanding a range of around 1000 to 3000 KM. The best-case scenario ranges that are sabre-rattled are certainly theoretical. They do not have ICBM capability and are not capable of launching an ICBM or exiting the Earth's atmosphere, but they do threaten Japan.
Strike capabilities reaching North Korea do indeed exist. All three legs of the nuclear triad may strike a North Korean target, but airplanes must sortie from the Pacific (leaving them vulnerable to detection, interception or suppression) or follow the course of a land-based ballistic missile strike which by necessity must pass over Russia, China, or much less feasibly, India.
As you mention we do have ICBMs that are capable of striking basically and literally anywhere on the planet. This is not really enough, because those ICBMs must pass through many, many layers of enemy strategic defenses.
From a nuclear arms point of view, its likely that our longest range reach-out-and-touch-ya' weapon systems really need to carpet-bomb entire regions and cities to achieve their designed operational objective. In effect, we're going to lose too much accuracy as well as ordinance to shoot-downs, reducing our effectiveness in the vicinity to a near minimum. Minimum lethality is quite lethal, but considering a maniacal super-villain's armored bunker really and truly is what we need to begin constructing a realistic view of the challenges set forth here. This analysis completely disregards the possible side effect of poisoning Seoul, South Korea with nuclear fallout as well as triggering a chain reaction of thermonuclear retaliatory strikes in a horrific reprisal of the 1914 assassination of the Austro-Hungarian Prince Archduke Franz Ferdinand in Sarajevo.
In short, its in a tricky spot. Luckily, the most danger they (North Korea) pose is to local Pacific naval operations, intense cold-war era artillery bombardment of South Korea (Seoul) or the possibility of a regionally effective ballistic missile. In addition to these threats, they also pose cybersecurity, money laundering and counterfeiting risks and of course, their people are starving in a totalitarian hell-hole regime.
I hope that one day there is an end to the pointless suffering of the people who live in North Korea.