Calling them "key signatures" is misleading - they don't actually tell you the key, all they do is indicate which notes are sharped or flatted.   There's a conventional way of writing this, which makes it easier to interpret. You can derive the key from this, but only by also looking at the melody and deciding where it is rooted, especially where modal versions are involved. When people first study music they don't usually come across modes, so a simple major/minor choice is easier to learn but can lead to a rigid way of thinking which may be unhelpful when you move away from Western classical music.

As someone who uses notation as an aide-memoire rather than for playing from, I find it helpful to denote A Mixolydian with two sharps and a naturalised C, rather than making all the Cs natural as they occur, or just showing two sharps which can be confused with D major or B min. ABC displays "A Mix" as two sharps, but the natural can be added.