As I type this, there are 4 beds in my house with "summer quilts" that I've made. None of them have batting. As described before, they are just tops and backs which were quilted to keep them together. They are the perfect weight for summer, I could not stand anything heavier.
I have a bunch of old quilts in my attic that were made by my mother and her contemporaries in the 1940's. None of them have any batting either. In fact none of them have the bindings that are typical now either. They all have the backs wrapped around to the front. That's the only type of binding that I use, by choice.