I think there is a certain amount of apples to oranges when comparing thick to thin airfoils. If you really want to take it to an extreme take a look at some of the ultra-lightweight microfilm models and their single surface undercambered airfoils. Thick airfoils existed before WWI. At least one of the Antoinette monoplanes had a (relatively) thick airfoil. While there is no denying that more modern airfoils have generally speaking better performance the thin undercambered airfoils worked well given the materials and structural science of the day. They were flown at a different range of airspeeds. I have seen a thin airfoil on a scale Demoiselle (spelling?) that was capable of flying very slowly with just a .40 size motor. An undercambered airfoil isn't going to do a good job of screaming around the sky like a Yak or a Mustang but if you are building a pioneer aircraft that is going to put around at a scale like speed they work pretty good. The fact that some of their structure is external of the wing skins in the form of struts or bracing wires can be intimidating but it is possible to cheat a bit with materials that are now available such as carbon fiber.
Regarding the Clark Y, I'm not that sure that all of the airfoils labeled as such really are true Clark Y airfoils. It is pretty easy to call a flat bottomed airfoil with a rounded nose a Clark Y. As TFF notes it is a comfortable label. Abufletcher describes that it is easy to build, it's also easy to draw. It was the first airfoil I ever learned to draw. As I was rambling a thought occurred to me related to being comfortable with the flat bottom air foil as it relates to high fashion. You can be comfortable or you can look good and you look marvelous.