They drew the consonants from the mouth. The letter for k is a tongue humped against the back of the palate; the n is the tongue tip up behind the teeth; the m is just a mouth, square and open. Then the vowels out of three strokes — a dot, a flat line, an upright one — and you can assemble the lot on a counter with matchsticks. The Hunminjeongeum, the book that set it out in 1446, carries a postface claiming something like: a wise man will learn it before the morning is over, and even a slow one in ten days. Boastful, maybe, but people keep testing it and it keeps roughly holding.
Most writing systems drift into being; somebody's tally marks get borrowed by somebody's clerk and four hundred years later you have the alphabet I'm typing in. This one was sat down and worked out, under Sejong, with reasons given for every shape. I've two Korean primers in the shop, both secondhand; the older one has a child's wobbling vowels in the margins, which is the best proof I own. The North keeps the day in January, the South keeps it in October, and the letters don't mind.
Choe Manri put his objections in writing in 1444: abandon Chinese characters, he argued, and Korea drifts loose from civilisation. Yet much of the earliest printing in the new letters was Buddhist — the life of the Buddha, and the songs for it, commissioned in grief after the queen died. Devotional books travel, which did the alphabet no harm.
Jun, the holiday itself has had a wobbly career: the South dropped it as a public holiday in 1991, on the argument that the country had too many days off to be productive, and restored it in 2013 after years of petitioning. The letters, as you say, didn't mind either way.