I've seen plenty of badly designed mobile websites over the years and these sites seems to have turned out okay - most mobile browsers keep the option of "Request Desktop site" very accessible for a good reason.

The worse case I've seen is a site in which every page crashed Mobile Safari without fail regardless of which version you ask for. It was eventually fixed but I never figured out why. If the sites are just running some script without checking then the admins have failed their line of duty.