A significant number of well-regarded writers (and many more long-forgotten writers) began their careers during the pulp era, pounding out short stories for a penny a word, or less. Their work filled dozens of pulp-era magazines with all manner of genre fiction. While the pulp era is long past, short story writers can still generate a respectable income writing short fiction.
It isn't easy, though. It requires the ability to produce a lot of words in a short amount of time and in multiple genres. Writers unwilling to do this--especially those unwilling to venture outside the realm of a single genre--will have difficulty placing more than a handful of stories in any given year. But those of us who don't mind bouncing from one genre to another like a pinball can find receptive markets every time we turn around.
I can, without much effort, name markets that publish a combined total of more than 1,000 short stories each year. I can probably--though it would certainly take a bit more effort--name markets that publish a combined total of more than 2,000 short stories each year.
I'm selling a short story each week, so I'm only filling 50 or so of those 2,000+ slots. Surely there are other writers doing the same. If you're out there, raise your hand. We just may be the modern pulp writers.