Sparring is not a perfect simulation of competition, but it's a reasonable facsimile. If you are trying to produce competitive fighters (boxers, kickboxers, MMA fighters, etc.), your students will need to spar at some point. How much and how often will vary (I honestly believe that more experienced fighters probably need less sparring), but sparring is a necessary part of contest preparation for most fighters.
For students who have no intention of competing, sparring will probably be the closest they ever come to doing so. That can be helpful for giving them some insight into what competition is like, and perhaps give them an appreciation for how challenging competition can be.
Sparring can help develop timing, targeting, range, and proximity sense. There are, of course, other ways to do it, but again, doing it a field of resistance helps create some unique learning opportunities. Some of those skills will translate to other arenas, including self-defense. I have a pretty good sense of range and distance, and I attribute it to spending a lot of time sparring.
Sparring can help develop qualities like pain management and mental toughness. Used properly, it can be a way of confronting fears (used improperly, you can damage someone for life. So it goes.). Getting hit when you aren’t expecting it or ready for it is a different sensation than getting hit when you know it’s coming. There’s a skill to taking a hit and keeping going, one that translates outside of the ring.
Sparring is a form of conditioning. You can be in "great shape" and not make it out of the first round of sparring. The slightly out-of-shape guy who whoops up on people in the gym for round after round is practically a cliché. If you want to be in shape to fight, practicing fighting is a good way to go about it.
It is worth paying attention to the flip side of that cliche: you can be "in shape" to fight, and still be at an unhealthy weight. At my heaviest (over 200 pounds), I was still capable of sparring for multiple rounds. Today, I'm 30 pounds lighter, and much, much healthier. If health is your priority, sparring won't be enough (really, it's not even necessary, but let's say you want to).
Sparring and Self-Defense
Speaking of subjects that have had reams and reams written about them...
Sparring is not the same thing as self-defense. Full stop. It is not even a simulation of self-defense. If what you are doing looks like a sparring match, you are probably not defending yourself. Tony Blauer and Rory Miller (among others) have both written volumes on this subject. Go check out their work.
Just because something is not a directly simulation of self-defense does not mean it has no value in self-defense. Plenty of people advocate strength training, but no one ever deadlifted a person in self-defense. Being strong helps. Being fast helps.
There are lots of things that might turn out to have value during a self-defense situation that are not direct simulations of self-defense.
Sparring can teach you about dealing with pain, frustration, and failure. It can teach you how to hit someone, and how to get hit.
If the only thing you are concerned about is teaching self-defense, you might not need to have your students spar.
On the other hand, life is about more than self-defense, and sparring is a training tool that can offer some carryover to self-defense, and provide other benefits for you students as well. It certainly CAN have a place in self-defense oriented curriculum.
I’m sure there are a bunch of far-to-serious-about-themselves martial artists who have now given up on me, but look, sparring can be a lot of fun. Part of the reason people like to do it so much is because it is fun. It is challenging, it gives you an endorphin rush, and you can feel pretty awesome when you’re done.
There are worse reasons to dos something than fun, especially if there are other benefits on top of it.