Mr. Can't Died
Grant writes:
What’s the difference between drunk and drunken? If you dig through the linguistic corpora, or collections of texts, you’ll find that we celebrate with drunken revelry and break into drunken brawls, but individuals drive drunk and or get visibly drunk. Typically, drunken is used for a situation, and drunk refers to a person.
It's relatively recent that people drive drunk, rather than drive drunken, and my ear still tells me that drive drunk is a coarse illiteralism. As you point out in this episode, drunk is only an adjective, and one may bee a drunk driver, but not drive drunk according to the traditional rules of this language. (I recognise that things change; when people defend the traditional definition of marriage, I point out that the traditional rule was that both had to be adults of the same race, and before that, both adults of the white race, and if you go back to the Common Law, both whites at least 8 years old. But my ears still thinkj driving drunk is literally, as well as morally, wrong.
In 1960, for instance, drunken driving was about 20 times as common as drunk driving, and it wasn't until about 1980 that driving drunk became more popular. MADD was formed in 1980, and you may feel free to scandalously quote me out of context: MADD (Mothers Against Drunk Driving) is responsible for the popularity of drunk driving. It's the Winston effect: get enough mentions in the media (by paid or unpaid mentions) and illiteralisms sound good like a cigarette should.

'typically' is a very key word above.
The choice between drunk and drunken is also idiomatic:
to drive drunk (not drunken)
to swear like a drunken sailor (not drunk, though: A bunch of drunk/drunken sailors )
One thing Grant didn't mention (is it possible he didn't know?) is that the expression in the UK is drink driving, which sounds totally ridiculous to my US ears.
On the other hand, the Brits are also responsible for the best bit of wordplay in which, for the joke to work, the state of being intoxicated must be called drunk and not drunken, this conversation between two people, one of whom is about to experience traveling through hyperspace for the first time:
Ford: "It's rather unpleasantly like being drunk"
Arthur: "What's so unpleasant about being drunk ?"
Ford: "Try asking a glass of water"
From The Hitchhiker's Guide to the Galaxy.