I actually don't think many people read from publications for the sake of supporting people writing in them. I read and comment on everyone who posts something in my publication, but that's just a courtesy as it's small. The collection of stories I hang together in my other publication is just a way of presenting them and finding them. Giving things a home where I can find them later.
I think the biggest strength of publications is that sometimes people do go there looking for something to read, and you never know, it might be your lucky day. But most of the time, I'd say you only get one extra read, maximum, compared to self-publishing.