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.
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.
Granted tuning an organ is an all day (or even multi-day) problem, but it is perfectly possible to change temperament. Tuning a piano to change temperament will take a skilled tuner some time as well.
harpsichord - I knew that, but couldn't think of the right instrument...