I have a 28mm lens with a symmetrical design that shows no distortion

I agree that, in general, wide angle lenses are harder to design in term of distortion control, but it's not a god given rule that all lenses wider than 50mm have to show distortion

Here is a 28mm with virtually no distortion: https://www.lenstip.com/233.6-Lens_review-Leica_Summicron-M_...

Here is the same with a 35mm: https://www.lenstip.com/610.6-Lens_review-Voigtlander_Apo_La...

Here is a 50mm that shows as much distortion as the two I mentioned before: https://www.lenstip.com/205.6-Lens_review-Leica_Summicron-M_...