why does it not make sense to talk about the wavelength of white light?

Answer 1

White is not a separate color with its own wavelength.
White light is all the colors mixed together.
When all the colors arrive at once, we see white.

Answer 2

White light consists of all the colors of the rainbow -- red, orange, yellow, green, blue, indigo, violet -- and each color has its own wavelength. In other words, white light is a kind of jumble of various wavelengths and has no separate wavelength of its own.

Answer 3

In the same way it makes no sense to talk about the height of a crowd.