I can't speak to literary publications, but in the SF/F field some of the magazines which receive the most submissions are also the ones that respond the fastest. Lightspeed and Clarkesworld are known for processing 600+ submissions a month each and yet managing to get back to authors in well under a week on average. Their slush readers are unpaid volunteers, just like elsewhere.
What that means to me is that it CAN be done. A magazine, even the one inundated with submissions due to their popularity and/or pay rate CAN get back to authors quickly. Just like any other business, it will do so if it is well organized.
But keep in mind that most editors only do what they do because they love fiction. And while they might be wonderful editors with great tastes who publish award-worthy stories, they're lousy managers. They don't KNOW how to streamline the processes very well, how to recruit the right slush readers, how to manage people and get the best possible results from their teams.
This is not a rant or a knock on the editors. When I go to a fine restaurant, I don't expect the head chef to be hiring waitresses, managing reservations and making sure the bar is well stocked. I expect the restaurant manager to do this, while the chef oversees the kitchen to make sure I get served an excellent meal.
Unfortunately there isn't a lot of money in short fiction and in most publications the editor and the manager are the same person, and that person has a "real life" job to worry about as well. And *that's* why submissions to some venues take so long.
I only submit to magazines that pay well, so maybe tiny little places are different, but no magazine I've ever dealt with took as long as they do because they lacked organization. To the contrary. Magazines that take the longest are often far and away the most organized.
I try to avoid most magazines that uses more than one unpaid slush pile reader, and many, many, many, many magazines out there do not use unpaid slush readers at all. Many that do take on just one. This is smart. Using several is not smart.
This aside, it's just not true that organization alone always has
anything at all to do with response time. For some magazines, submission time takes so long at many mags because a six hundred submission month just never happens. If it did, you'd wonder why five or six thousand writers suddenly stopped submitting.
For other magazines, you have the editor and the assistant editor, if you're lucky. No other slush pile readers, paid or unpaid. You have, if you're
lucky, four hours per week to read submissions. Most of this time is spent reading submissions form writers you know. You can't organize time that doesn't exist.
And getting back to writers in a week or less is usually NOT a good thing for writers. No matter how well-mentioned, too many chefs in the kitchen means inconsistency, and several slush pile readers always, in my experience, means inconsistency. Too much speed also usually means too little time spent per submission, which is also bad for writers.
Be that as it may, nowhere do I know what you say to be the case. Submissions take as long as they take for very good reason, and lack of organization plays no part in it.
And, really, submissions times are not unduly slow. Most writers are just unduly impatient.