Certainly, a good, prolific writer could beat minimum wage if he included non-fiction in the mix. In the case of pure fiction, however, I believe beating minimum wage from short fiction alone would be extremely difficult for any writers but an elite few who have made huge names for themselves. And for science fiction, fantasy, or horror it would be even more difficult. For science fiction, it needs to be written in the current style that the pro magazines are interested in (not just good, but written in a certain style). For fantasy, it would need to be literary in style (no traditional sword and sorcery or high fantasy). So those are considerations that go beyond simply being a "good" or "bad" writer. It becomes a matter of matching your style to the few available professional markets, and even if you do that flawlessly, you're still looking at coming in below minimum wage. The writer (good and prolific, or not) who chooses Tolkien-style fantasy, Howard style sword and sorcery, Bradbury-style science fiction, or any style of horror is not even going to sniff minimum wage, in my opinion.
I don't know about fiction for adventure and humor magazines or what have you, so perhaps it's possible if you work that angle.
Regardless, there are plenty of good reasons to write short fiction. And there are very respectable paying markets. It's important, however, not to quit the day job.
Well, I've never included nonfiction in the mix. It's possible to earn an extremely good living writing short nonfiction, and I know several short nonfiction writers who earn fron sixty to one hundred thousand per year. Not too many can do this, but many, many nonfiction writers do earn a worthwhile living.
Of course you have to match the short stories you write to the existing markets, but there are far more paying markets out there than most writers realize. I would, however, add "versatile" to good and prolific.
From my experience, good sells, no matter what "style" magazines generally publish. Often, in fact, going against the style a magazine usually publishes will get you in faster than going with the common style. I've made more sales by consciously going against the usual style and content of a magazine than by going with it. I know an SF writer who has sold just about two dozen stories in teh last four years, writing very much part time, and his stories are nothing at all like the style and content the SF magazines usually run. He sells because he's good, and because he's different. He gives editors something they aren't getting elsewhere.
Before submitting to a magazine for the first time, particularly a high paying magazine, I read at least a dozen issue, more if I can get my hands on them, and the question I ask myself is not "What do they publish, and how do they like it," but "what haven't they published, and what do they want that they aren't finding in the slush?"
I've read a lot of slush piles, and by and large, what you find will be story after story after story that tries to mirror the content and style the magazine usually publishes. This works, if the story is exceptional, but what every editor loves to find is a story that does just the opposite. You always want good story and good character, but it's a pure pleasure to find a story that's unlike anything else above or below it in the slush pile. Originality in style and content really do matter.
Nor do I think it's a matter of having a big name. I sold back to back stories to Sports Afield, one for $1,000 and one for $800, at a time when no one anywhere had a clue who I was. The editor bought the stories out of the slush purely because he liked them. Total writing time for both stories was just about exactly eight hours.
For me, earning money from short stories is about the hourly wage, rather than about how much the market pays. Minimum wage iswhat, $7.25 per hour now? That's fifty-eight bucks per day, or $290 per week.
If you're versatile, a LOT of three hundred to four hundred dollar markets are out there, and it almost never takes me a week to write a short story.
If you can also hit some of the twenty-five to fifty cent per work markets, you can make from two to four weeks of minimum wage with one sale, which gives you a nice cushion.
As I said, you have to be versatile, and you have to keep your eyes open. I picked up a children's magazine, had never written anything like that before, but read the stories, sat down and wrote one in a few hours, and they paid me three hundred dollars, plus seventy-five extra bucks for one time, non-exclusive reprint rights, for twelve hundred words. That led to some nice money from other such magazines.
Reprint rights to non-competing markets also add to the tile in a nice way, and with little to no extra work. I've had stories make considerably more in reprint sales than they originally sold for.
You do have to be good, prolific, and versatile, but if you are these things, and if you can make a habit of giving editors what they aren't getting elsewhere, there's more money in short stories than most think.
I suspect more fiction writers would earn a decent amount of money from short stories if they didn't turn to novels. There's a lot more money in novels, and when a writer starts selling novels, his short story production usually goes way, way down.
Funny, but way back when, I did quit my day job based on a short story sale. Well, based on three short story sales, but I didn't know the other two had sold. That first story I wrote sold to a national magazine for roughly as much money as my day job paid in a month (Minimum wage was a LOT lower back then), and I said to heck with it.
Probably not a smart thing to do, and I sure don't recommend it, but it does depend on what your day job is. If you're pumping gas, or, as I was, shovelling coal and picking up heavy objects here and sitting them down there, for minimum wage, and know you can get another such job without trouble, you can take a chance without much worry. But if you're earning great money and have great benefits, quitting your day job is, well, stupid.