There used to be keyboard instruments with double black keys, but they never really became popular. That's why Equal Temparament was devised, so that pianos could be roughly in tune, though as Pablo Casals said:

Do not be afraid to be out of tune with the piano. It is the piano that is out of tune. The piano with its tempered scale is a compromise in intonation.

There are similar problems with other ET instruments. It took me a long time to get used to the sound of traditional tunes being played on accordions, as they don't play the same notes as fiddlers, or for that matter, pipers. Traditional singers too, will have a tendency to sing pure intervals rather than ET. And then I came across blues which uses yet another scale system......

As for A=440, a lot of older fixed pitched instruments are tuned differently, and I've heard that American orchestras are starting to tune to A=442.