I have no martial arts experience, but wrestled for 4 years in high school. That's many hours of training in wrist control. Someone tried to stab me once. Right in the chest with a big knife. It wasn't a pre-meditated attempt, but it was an attempt (I was stopping a suicide attempt). I instinctively caught their wrist and no one was harmed.
My dad was also a wrestler and has multiple stories about taking down martial artists who tried to pick on him.
This is a large topic.
Speaking loosely, even any generic high school wrestler would probably stand a pretty good chance against a classically trained karate/kungfu/tae kwon do fighter with similar training time...provided that they're sturdy enough to take one or at most two strikes before the fight goes to the ground.
There are several reasons for this, but at the heart of it is that lot of classical eastern martial arts focus exclusively on stand up fighting, and a lot of the power of their attacks comes from the way they interact with the ground. A proper karate punch generates only a very small portion of its power from the arm. Most of it comes from the hips, and the act of driving one leg into the ground with your entire body behind it into a punch.
If you can take a karate fighter off his feet, not only have you put him into an environment he hasn't much training in, you've immediately removed the majority of the power behind his attacks. You've invalidated most of his training simply because it can't be done from the ground.
I also appreciate that someone (I think it was LordBucket?) commented on the importance of grappling. I
can attest to that. Weapons have been mentioned often, and grappling would be your best defense there.
Also complicated, but speaking from my own experience, I think we need to distinguish "grappling" in the sense of joint and/or pressure point manipulation, from "throwing" techniques in the sense of smashing your opponent into the ground, and from "wrestling" in the sense of both parties on the ground attempting to render one another prone.
Joint manipulation is a popular thing, but...in my opinion, it is highly over rated. An
awful lot of joint manipulation techniques can be completely avoided just by rotating an arm or shifting your weight by a tiny amount. There are also a significant number of people on whom pressure point techniques just flat out don't work. They either don't have the nerves they're supposed to, or they've grown enough muscle over them that it's impractical to get to them.
Unless you're significantly bigger and stronger than your opponent, I'd advise anyone against depending on any kind of joint or pressure point manipulation technique working like you want it to. I cannot count the number of times I've been on both the giving and receiving end some some technique during a training session that simply
did not work because of the person it was being used on. If you do grappling for any length of time, or if you're simply bigger and stronger or even something as simple as having wider wrists that somebody...so many factors can make it completely trivial to avoid an awful lot of these techniques.