Not just that, but you could use the same sheet of music (if you went pure jianpu with no other notation) for guitar, bass, accordion, xylophone… anything that isn’t a transposing instrument (like clarinet for example).
Well, I think having two categories, major and minor, is a necessity, and therefore “1” would need to shift. True modal pieces really aren’t all that common though, but if I came across something like Lydian, I’d just keep it as major and throw in an accidental for the augmented fourth.
There is a post here where modal key signatures were discussed, whether it made more sense to write C Lydian as G major, for example, or C and use F# where needed in the music. Getting a little out into the weeds from this topic, but if you’re curious: