Why must programming be so universal? Look at the number of people who would balk at a simple task like replacing a plumbing fixture or a light fixture. This isn't implying that these people are 'stupid', it just isn't a skill that they have decided is worthwhile to learn. Changing the oil in your car isn't hard to learn, and certainly isn't filtering out the stupid, but there are just a lot of people who simply don't feel it is worth learning how to do. And programming isn't any different--it simply isn't a universal enough skill. Sure, it is essentially required to know basic arithmetic and literacy to function in a modern society, but I don't think that programming is a skill that will ever be on that level.
Maybe that argument could apply to typing, but I'm not sure that even the ability to use a keyboard will be that kind of universal required skill in my lifetime.