What do those jackets have? Big hip pockets. What fits perfectly in those, hardly even affecting the drape, with enough room to spare that they can slip in and out effortlessly? Slim little pulp fiction books. Hell, many are even big enough for a volume of Magazine of Fantasy and Science Fiction to fit OK. Can't cram a glossy in there, but pulps? Yep.
Plus, yes, there were no cell phones, but if you want to carry a book today, where do you put it, if you don't have a bag (and even if you do, that's not convenient, is it?)? Well, on your phone, as an ebook, since that fits in a jeans or trouser pocket, and practically no dead-tree books or e-readers do... oh but look, you have some notifications! And there goes the 15 minutes.
Women often carry purses. And who still reads? It's largely women. I'm sure there are other reasons, but—hmmmm.