"Drop-dead gorgeous" seems to have been with us since just 1985. A piece about Michelle Pfeiffer in Time in February of that year says:
"Trim, smart and drop-dead gorgeous, Pfeiffer has been nibbling at stardom since her stints in Grease II and Scarface."
The phrase struck a chord and there are many references to it in newspapers and journals from very soon after that.
It didn't arrive out of the blue. The term "drop dead", meaning excellent had been around since at least 1962. In The New York Herald-Tribune, January 1962, we have:
"Fashions from Florence not drop-dead. For almost the first time in history Simonetta failed to deliver an absolutely drop-dead collection."
It got picked up as an intensifier for various things, as here from the Washington Post, July 1980:
"For drop dead chic food, Harborplace has a sushi and tempura bar."
Of course, "drop dead" has also been used as a term demonstrating dislike for some time. This originated in the US in the 1930s.
Phrases tend to be coined to deal with things that people engage with frequently or consider important. There are hundreds of phrases to do with topics like God, money, sex etc. It's hardly surprising that death scores highly too and that 'dead' is one of the words that appears in many English idioms. Here's a selection that begin with a, b or c - there are many more:
As dead as a dodo
As dead as a doornail
As dead as mutton
At the dead of night
Back from the dead
Better dead than red
Bring out your dead
Chivalry is not dead
Cut out the dead wood
The use of the word dead in English idioms is an example of how difficult a language it is to learn for non-native speakers. That's perhaps what could be expected from a language that has nine different ways to pronounce 'ough':
through - oo
though - o
thought - awt
tough - uff
plough - ow
thorough - uh
cough - off
hiccough - up
lough - ock
Even supposing someone understood the word 'dead' (and there are at least 31 meanings for dead just as an adjective), that doesn't help in understanding idioms. These rely on a knowledge of context that goes beyond the dictionary; for example, how is it that people who are "dead from the neck up" or "dead to the world", can be alive and well? Why is a "dead shot" to be admired when a "dead loss" isn't? Go into an English pub at closing time and you'll be asked, "are those drinks dead"? You might even hear someone claiming to be "in dead earnest".
If you learned your English as a first language, be thankful. If not, and when someone meets you they say "drop-dead gorgeous", don't be offended.
See other phrases that were coined in the USA.