What you state is, of course true. "Al divino botón" meant porpuseless, with out any real motive. It isn't used today anymore (2023).

But please note that, also in lunfardo, in 1973 'botón' meant 'policeman'.

So, "al divino botón" has a second, connotative, meaning: "to the dear policemen"

I watched María Elena Walsh performing live in Teatro San Martín when I was a child, about 10 years old. It might have been any time around 1971. I enjoyed the show, of course. All the songs seemed written for me. But, then, suddenly, she sang a song in a strange language (lunfardo) and I couldn't understand a single word, though I realized, confused, that all the grown-ups around me, including my father, laughed heartedly.

She certainly could use lunfardo.