All right, all right, here we go. These are reasons why one should write and seek to publish short stories, in order:
1. one enjoys writing short stories
2. one enjoys reading short stories
3. one can gain some benefit from publishing short stories.
If you’re writing short stories to "get your name out there", let me assure you that there are many many easier ways unless your short stories are superlative. (And yes, plenty of people publish some stories and then some novels, but that is not the same as saying that the publishing of stories contributed to the publication of the novels.) If you’re writing short stories to "practice" writing novels, please stop right now as this practice tends to lead to both mediocre stories and mediocre novels. (Which doesn’t mean you won’t make money or get awards or have little fanboys or anything, but you will stink up the place, regardless.) If you don’t like writing short stories and don’t like reading them, the benefits you can even hope to gain from publishing them will be even slimmer than otherwise.
The benefits of publishing short stories depend partially on genre. In science fiction/fantasy/horror, one of the benefits is the payment of anywhere from $25 to a thousand dollars or so. Generally, payments for stories fall somewhere in the low three-digits and there are some opportunities for reprinting or repurposing stories. Perhaps as many as a couple tens of thousands of people will read your story as well, which is both a psychological benefit and some level of commercial benefit—more solicitations, for example, and to a much lesser extent some way of having one’s novel looked at (not published!). Venues that do not pay very well or at all are generally not read by more than a few hundred people, many of them submitters. Thus, there is no value in publishing in most of these venues, especially since the editors are generally dim bulbs themselves, so anything they may have to tell you about good writing will likely be idiosyncratic at best or just wrong at worst.
There are exceptions, of course, and these are generally based around this or that particular marginal aesthetic (e.g., Lovecraftian fiction, contemporary versions of "classic" ghost stories, First World attempts at "literary fantasy", etc.) It’s not that these venues are widely read despite not paying well, but that they are closely read by some editors and other "important" people and that help with having a specialty press put out a collection, or almost winning an award, or republication in a best-of annual, or a soliciation to a larger venue, etc.