Some people seem to make the case that having some keys beat more than others (as is in the case in the older well-tempered tuning systems) is a feature not a bug. But on the other hand, the equal tempered tuning system seems completely dominant and rarely even questioned at this point. Historically, why was the change made to equal temperament given that the various keys would lose some of their unique character?
Partly to allow the same, diatonic, piece to be played at different pitches as @Tim suggests. But also, I think, because music started getting more tonally adventurous within the SAME piece. When you start wanting to visit (say) the mediant key as well as just the dominant and subdominant, equal temperament is a must.
Some people seem to make the case that having some keys beat more than others (as is in the case in the older well-tempered tuning systems) is a feature not a bug.
Yes, but I don't think that was ever a major consideration. Originally, all tuning systems just tried to give good approximation to just intonation (JI). At first just for a few neighbouring diatonic keys, which can be done quite easily. But then composers wanted ever more freedom for modulating anywhere, and thus we came to well temperament. That did allow playing in any key with acceptable error to 5-limit JI, but how exactly this error played out was of secondary concern.
Of course...sure enough, Bach, being the grand master of meticulous multiscale[pun intended] thinking, made an art (or science?) out of this effect itself with his Well-Tempered Clavier pieces. But, Bach is Bach, nobody else is. Maybe if he had written a detailed explicit treatise on how to use each of the keys in well temperament, that would have stayed longer. But most composers just took WT as, well, basically an approximation of the approximation that is 12-edo: they jumped to the opportunity of using any key they wanted and still getting an approximation to JI. And then it was the obvious next step to make that approximation literally the same regardless of key.
Simply so that any music could be played in any key and it would sound the same. Problem with tuning to another temperament means that pieces sounded particularly good in some keys, and particularly bad in others. And re-tuning often isn't a quick answer - especially on instruments such as piano!
Non-fretted stringed instruments, such as violins, trombones and voices are not really affected by 12tet, and will have a tendency to re-tune certain notes out of 12tet, so they sound 'more in tune'.
So it was more of a 'one size fits all' approach that won over - yes, always a compromise, a slight dumbing down if you like, but far more practical overall.
As a temperament junkie, I'd just like to humbly add to all the answers above that one way of looking at it is in terms of thirds and fifths: temperaments in Western music tend to be thirdier or fifthier. 12TET is almost as fifthy as it gets, two cents short of just is pretty good and a lucky coincidence of mathematics- but the thirds are pretty far off. 1/4 tone meantone is thirdier but hairier in distant keys. Just intonation further increases quality at the expense of quantity (of nice keys to use). All have their place.
I thought I didn’t understand your question before I’ve found the other answers voted up.
It seems that you know the different tuning systems and their problems and advantages.
So I thought answering this kind won’t be sufficiently.
Historically, why was the change made to equal temperament given that the various keys would lose some of their unique character.
The old tuning systems have been only useful for some keys on all those instruments that can’t be adjusted/ tuned while playing. So they sounded simply wrong in certain keys.
The unique character was described already by Plato and sustained even after the introduction of the well-tempered tuning system. But I could‘t find a consensus in all ths theories.