JS Bach did not use a piano either.
Because so much of music was written around the organ (e.g. vocal music sung in tune with a church organ) tuning was what it was.
The well tempered clavier is exceptional because it is an exception to the vast majority of JS Bach’s work.
Organs are and were tuned all the time. While he didn't have a piano, the organ was tempered in some way.
His well tempered clavier was a plea to give him organs that could play in any key. We don't know what temperament he used (there is plenty of debate), but it is clear he was trying to show how the key in his system changes the sound/mood of the piece - something lost in equal temperament.
My family has a harpsichord, so I've learned a fair amount about it, though I'm not the one who plays it.
Harpsichords went out of tune easily and quickly, so they had to be tuned at least as often as every performance.
The way I look at it, a musical scale is a technology. Often, a particular technology is chosen because it solves multiple problems with acceptable compromises. A problem for the harpsichord is that the musician has to tune it themselves, often quickly, to make it sound good enough for a performance.
We don't attempt equal temperament on the thing.