The earliest use of equal temperament was on fretted instruments with fixed frets. The ratio of 17:18 for the string length for successive frets is a good approximation to equal temperament. The errors were well within the tolerance of other intonation issues such as non-uniform gut strings, and the different amounts of string bending on different frets because of the height of the action.

Not all early fretted instruments had fixed frets - for example the frets on lutes were loops of gut tied around the neck and were adjustable.

It is probably safe to say that no keyboard instruments were routinely tuned in equal temperament for the first 1400 years of their history - there are mosaics depicting organs played by keyboards, and texts describing the sounds they produced, that date from 400 AD.

Equal-tempered tuning on a harpsichord certainly doesn't sound "better" for the historical style of playing. Harpsichord tone has more high harmonics than piano, which increases the difference in effect between just intonation major thirds and equal tempered. Most "serious" modern harpsichordists would use appropriate historical temperaments, and different temperaments for music of different periods. Harpsichords need much more frequent tuning than pianos, and harpsichordists learn to do it themselves, just like guitarists, string players, etc. Technically, it is much easier than piano tuning because the string tension is much lower, and a "non-expert" tuner is less likely to physically damage a harpsichord than a piano.

To answer Tim's comment, unequal temperaments did not *only* "sound better" in "just one key". For example, in the commonest meantone temperament used in the 16th century, where the tempered note names are C C# D Eb E F F# G G# A Bb B C, any major scale from two flats through to three sharps is "in tune", and in fact all those scales have exactly the same frequency ratios between the notes, so there is no problem with modulations within that part of the circle of fifths. But if you attempt to go outside that range and play an "Ab chord", the notes G#-C-Eb sound horrible, and so does a B chord with B-Eb-F#. 

The various "well-tempered" tuning systems devised in the 18th century were useable in every key, though every key had its own slightly different sound - and it is clear that from the music that composers like Bach made deliberate use of that fact. The typical patterns of harmony and counterpoint are different in different keys. Some of those "well-temperaments" were still used by piano tuners even into the early 20th century.

Some modern harpsichord music is (probably) intended to be played in equal temperament - for example this:

https://www.youtube.com/watch?v=iPgwF3G5i4k