The general interest magazines were pretty much the network TV of reading in their era. The chance of finding something you'd really love was never all that great, but there was at least some quality filtering, and they at least they were cheap. If half of the stuff in them wasn't any good, you didn't really care. Nowadays this role is pretty much filled by the internet, although the quality filtering is much less direct, and not as effective.
The problem in general with short stories is that by the time you know if the story is any good, it's pretty close to over. If you buy a novel series, especially a long one, at least you know what you're getting before you buy it. This can be somewhat overcome with collections of short stories by the same author, but even there the variation of quality is much larger than in a novel. Along with marketing costs being not strongly dependent on size, this has been pushing the market towards not only novels instead of short stories, but longer novels instead of shorter ones, and novel series instead of single novels.
I think the best way for most authors to make money from their short stories is to give them away free on the web. Use the page views to advertise themselves. Insert a blurb that says, "Here is a list of my books you might want to buy, here's where to buy them, and if that's too expensive for you, please pressure your local library to buy them."
The marketing of authors as brands is pretty dysfunctional at the moment, mainly because there isn't enough trust that the author and publisher will remain together. Look at the front of any book. If you just read a book you liked, you will frequently want to buy another book by the same author. There's going to be a list of books by the same author and the same publisher, but the books by different publishers aren't going to be there. You'd think the publishers could agree to list them, which would benefit everyone, but no, they can't.
This also makes a big difference in quality filtering. Publishers used to sift through all the junk in their slush piles. Admittedly this was easier before the invention of photocopiers allowed spam slush pile submissions, but if any author you find is going to be poached by some other publisher, why spend all that time picking through the slush piles in the first place? Except, when nobody is picking through the slush piles, isn't everyone just publishing whatever crap happens to be popular without trying to actually separate the good books from the bad?
Ultimately, I think we're going to wind up with some kind of narrowcast crowd-sourced literature reviewing system which actually works, but it doesn't seem to be developing very quickly.