Well, if you’re going to be that way you can change mine to “1961-1971”.
I would go with 1968-1977.
That gets me a selection of the San Francisco bands and a slice of punk bands covering the period when punk rock was starting to get some attention. It gets me what I think of as “The Golden Age of Progressive Rock,” which (IMO) is packed full of treasures. It gets me most of my favorite Zappa material, the Big Four Rolling Stones albums (the studio albums from Beggars Banquet through Sticky Fingers), Miles Davis’s early 70s stuff, Mahavishnu Orchestra’s original lineup, and most of Zeppelin. It gets me Bowie’s glam rock period and two-thirds of his Berlin trilogy.
What it unfortunately leaves out, among other things, is some Bowie (in particular, Scary Monsters and Outside), later Residents, later Jeff Beck, all of Miriodor’s and Sonic Youth’s albums, a lot of pre-1968 blues, and more. But if the choice has to be made, I guess that’s where I am.
1969-1979
1967 - 1977.
Mostly for the reasons all the other old farts listed above. Have to get to at least '77, because I couldn’t handle not having Rumours or Born To Run to listen to. Plus, Renaissance’s Live At Carnegie Hall was released in '76.
If I have Sirius in my car, I set it to Classic Vinyl. Also Classic Rewind, but I also move around sometimes Deep track, Beatles, sometimes Jimmy Buffett, and for fun - Yacht Rock.

I’d get tired of any modern decade very quickly. I’m already tired of most of them.
That’s the problem.
How many times have I said OK Google Play Nat King Cole? Or Doris Day? Or Louis Armstrong? Or Matt Monro? Or the Seekers? Lots and lots.
How many times Haydn and Beethoven? A lot less. So I feel I have to say 1780’s. But then I think of dozens of artists from the 1960’s I OK Google. No more yé-yé? So maybe I have to say the 1960’s.
This hypothetical is in the category of — there is no amount of money I would accept to do it,

No more yé-yé?
I’d agree if I could follow what you were talking about… you said you don’t request Haydn and Beethoven much. “So I feel I have to say 1780’s.” Huh?
Then the … yé-yé’s?
Heh, I remember when Petula Clark was a ye-ye.
For me, it’s a narrow call between 1985-1994 and 1986-1995. Now, the former nets me some classics by three of my four core favorite bands, including Fables of the Reconstruction by R.E.M., New Day Rising and Flip Your Wig by Hüsker Dü, and Tim by The Replacements. But the latter nets me Here’s Where the Strings Come In, a winner from my last core fave, Superchunk. Plus, I was in college, and I would think music that I discovered at that age might ultimately be more meaningful than music that came out when I was not even a teen.