If you were to write something out that was, for example, in C mixo... Would you just make the key sig as C major and flat the B's whenever they come up? Or would you put the Bb on the key sig and possibly lead to some confusion as to if the song is in Fmaj instead?
as common as mixolydian and dorian seem to be, for the root key of songs, still key signatures tend to be immediately interpreted as ionian or aeolian. This seems kind of disappointing, but, to be fair, it is important to have an obvious way to tell someone what the real root key of a song is. Weirdly, most of the time, the key signature seems to be used to display this info AS IF it were ionian or aeolian, and then rudely use accidentals all the time. which feels kind of sad/wrong, but it happens. But actually, if you write 'C mixolydian' on the top of the page and then do it with a 1 flat key signature, i don't think anyone will mind