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.
By "tuning was what it was" I did not mean that JS Bach's organs were out of tune with themselves. But rather the obvious thing that pipe organs can't be retuned to arbitrary temperaments in a practical manner.
And to be clear, Well Tempered Clavier is generally believed to have been written for harpsichord not organ. There is not more evidence that it was a plea than that it was simply JS Bach writing experimental music for the latest technology.