Submitting
Submitting over and over until an editor buys something is a good practice. It's the best way I've found to get published, assuming you do have the talent. And it's been going on a long, long time.
William Saroyan received close to 4,000 rejection before selling a story. When he did sell one it was because he sat down with the intention of writing and submitting a story every day for a month, all to the same magazine. About two third of the way through the month, he wrote a story called "The Daring Young Man On the Flying Trapeze" and a legend was made.
More recently, Joyce Carol Oates received thirty-nine rejections from The Atlantic Monthly before convincing C.Michael Curtis to buy one of her stories.
There are magazines, such as The New Yorker, that want you to limit submissions to a couple per year, and other magazines that ask you to wait until you hear from the first story before submitting a second, but I've never known an editor to get mad and reject a writer out of hand because he submitted one too many stories. An editor who would do this is in the wrong line of work.
At the very least, a story a month should do no harm pretty much anywhere, and I've certainly submitted more often than this without getting in hot water. Or even lukewarm water.
As for readers, most large magazines, and some smal ones, have a first reader or two. At large magazines, these are usually assistant editors, and the same reader will probably read your stories far more often than not. Few, if any, magazines can afford to have people solely devoted to reading manuscripts.
Now, if you're a truly lousy writer, editors and readers aren't going to pay much attention to your manuscripts, but this is true whether you submit a story per week or a story per year. If you're any good at all, most editors look forward to reading your next story in hopes that this time it will fit the magazine well enough, and be good enough, to buy.
Too many writers seem to be a bit afraid of editors, and build walls where there should be open space. Editors aren't the enemy, and a good editor always looks forward to another story from a writer with any talent at all, even if he never buys one of them.