Note: This answer clearly misses one important element being sought - the story does not take place in the future. I'll leave the answer here, though, while we keep looking for the right answer.
"The Invisible Man" by G. K. Chesterton may fit.
There's supposedly a scifi story from the 1890's-1910's era about a mystery set in the 21st century where the solution is that the milkman did it (just showing how unlikely people thought that milkmen would disappear.)
It was published in 1911
It's science fiction, in some sense - it has robot servants!
"I suppose you've seen on the hoardings all about this 'Smythe's
Silent Service'? Or you must be the only person that hasn't. Oh, I
don't know much about it, it's some clockwork invention for doing all
the housework by machinery. You know the sort of thing: 'Press a
Button—A Butler who Never Drinks.' 'Turn a Handle—Ten Housemaids who
The mailman did it
“Nobody ever notices postmen somehow,” he said thoughtfully; “yet
they have passions like other men, and even carry large bags where a
small corpse can be stowed quite easily.”
The postman, instead of turning naturally, had ducked and tumbled
against the garden fence. He was a lean fair-bearded man of very
ordinary appearance, but as he turned an alarmed face over his
shoulder, all three men were fixed with an almost fiendish squint.
Mailmen haven't disappeared, though.