all light is Rayleigh scattered, it's just that short wavelength light is scattered more. The bluest light we can see has a wavelength of about 400nm while the reddest has a wavelength of about 700nm, so there is a roughly a factor of ten increase in the scattering going from the red to the blue end of the spectrum.
So the light we see from the sky isn't a pure wavelength, it's a mix of all the colours but weighted towards the blue end of the spectrum. For the sky to be purple we'd need the scattering of purple light to be much stronger than red light, not just a factor of ten.