A colour distinction between the squares is desirable. Any contrasting shade is preventing confusion. Has nothing to do with the colour of the pieces.
There is an ivory set in green and red, and what about silver and gold squares ?
Be glad the lighter coloured queen can be placed on all squares (as can the darker one) !
I doubt your first line (...better...not...), any prove ?
Moreover your last line refutes your statement, okay ?
In classical openings and themes. I see the queen is better to be placed in its own color..,say white Q will not move to black sqr. Unless we get some tactical positions to gain material.