Without training, people who fight very frequently end up in a clinch or on the ground. (This is common for people who train in non-sparring, non-grappling arts, too.**) It's just a natural outcome for a fight, unless you're proficient in grappling.
In most cases, one cannot stop grappling without...drum roll...grappling.
You might be supremely lucky and catch your opponent with a knee, or knock them out with a punch before they get close. It works, sure, but certainly not every time. What's the chance of throwing that knockout punch? One in ten? Twenty? Five hundred? There's good reason to take that chance, but no good reason to rely on it.
In contrast, the high-percentage options for defending takedowns--the ones that work against people very good at takedowns, pick-ups, trips, and throws--are themselves grappling:
- A well-executed sprawl works even against good wrestlers, as Tank Abbott showed UFC fans back in the day.
- The hip block, as learned in judo, is another fundamental. Footwork and posture learned in that art, as many other jacket wrestling styles like Sambo, is key.
- Detailed knowledge of the techniques going to be used against you (e.g. double-legs, foot sweeps, hip throws...) is vital. Defense is contained in understanding offense.
Notice that all of these involve copious actual grappling. Whether judo, Brazilian jiu-jitsu, freestyle or Greco-Roman wrestling--and there's significant overlap and carryover between all of them--you'll need to learn the techniques and practice them against a fully resisting opponent in alive drilling, in-class rolling/randori/wrestling, and competition.
Like Einstein, let's try a thought experiment. What would it look like if we tried to train stopping the takedown without training grappling?
First, we'd be using an awful attack. It's foolish to assume that a non-grappler, totally untrained in the double-leg takedown (or whatever), could execute one as well as someone who drills it day in and day out. Your takedown defense trained on that non-grappler would be weak and untested. (Many aikido instructors recognize this as a problem, since it's common in that art to train against strikes thrown largely by non-strikers.)
Second, what would it even mean when I don't knock my opponent out while defending the takedown? He grabs my shirt, and I...am not grappling? Surely I am grappling, however poorly. I can't expect to go for the grab-defense wristlock (or the knee strike from the clinch) if I ignore the fact that he's tripping me. I'd get tossed on my head in an instant.
The point is that we don't always get to decide where the fight goes. If he gets lucky, or is faster, or catches me by surprise, guess what--I'm grappling whether I like it or not. If I don't even know the terrain of that phase of the fight, I am bound to do poorly.
I could rely on hail-Mary eye-pokes and knees to the groin. However, nothing stops my opponent from throwing those back at me. Plus, he's more likely to be better at doing so, since he'll be on top, or choking me, or at least have a better idea of where we are and what matters. So that sounds like a bad idea.
Third, who do I trust for grappling technique? The boxer, who hasn't faced more than a half-dozen takedowns in his life...or the Samboista, who has a mean ankle pick and has competed numerous times (even if only at the local level) against people skilled at throwing, pinning, and controlling the grappling phase of the fight? I'd prefer to learn from the Sambo guy.
So we've concluded that we should go to a painter to get our house painted, instead of the plumber. Great. But which painter?
Wrestling, playing judo, training Sambo or BJJ or Greco or any other grappling-only option is good. That's important to gain a base in the fundamentals. However, it might be optimal to train MMA, san da/san shou, or another art where grappling is integrated with striking. Note, however, that best results will always be obtained with schools that train hard: sparring or wrestling every class, and entering competitions at least a few times a year.
Tim Cartmell's Ground Proofing DVD, developed with the express purpose of giving non-grapplers the minimum grappling skills and drills necessary to prevent, control, and exit the ground fight, might be a great fit. Tim is a second-degree BJJ black belt, as well as lineage holder in multiple traditional Chinese martial arts and a champion several times over in both BJJ and knockdown kung fu tournaments.
** As happened to two prominent Wing Chunners, Emin Boztepe and William Cheung:
He was struggling like a wounded mule because he had no countering
technique against the headlock. Because of the slipperiness of the floor
and my shoes, I was sliding around like I was on roller skates. At that
time, I started slipping, and then he fell as well. He was more or less
lying on top of me. Then he was sitting on my stomach, and tried to throw
a few punches