"This sort of nonsense" seems like no big deal, and really it isn't when isolated. But consider that guys like him exist in droves all over the world, and they've all been raised to think "hey, it's one little joke, what's the big deal? Get over it, crybaby."

So they make the jokes. Each time they do, it's no big deal to them, because hey, it's one joke. Then the next guy does it, then the next, then the next, each time it's just one joke, what's the big deal?

It goes on like this every day. Kids grow up seeing that it's okay to say that sort of stuff about women, because hey, it's just one joke. Haha, look how they're getting so worked up over just one joke!

But it's shitty comedy. There are a billion, billion jokes he could have made. Instead he said "women can't drive, har har, amiright guys?" It's pig headed, ignorant, and not even remotely funny. It's not even a pun, he's just literally saying women can't drive. Ultimately all it is is permission for more pig headed people to say ignorant, thoughtless things that only amuse ignorant thoughtless people, and generate more ignorant thoughtless people.

So, yes, you're correct. Isolated, without cultural context, this kind of thing is innocent, if a bit dumb. A drop of water splashing on you is no big deal, get over it. But when ten thousand other ignorant assholes are each squeezing their drops onto you and going "it's just one drop, get over it!" you're being blasted with a goddamn tidal wave.

This isn't about this guy, this one time. It's about the fact that he's perpetuating ignorance and stupidity, and by letting him spread the idea that doing so is no big deal, and that the targets of his ignorance should get over it, is just making things worse. So, should we run this guy out of town? No. Should we blame him for the greater issues of society? Not at all. Can we tell him "shut up, you're not being funny, you're being an asshole"? Yes we can.

TL;DR: Alone, his joke is innocent enough, though more than a little stupid and uninspired. But it isn't alone, and women shouldn't have to go their whole lives being mocked then told to get over it because it's just a joke. The guys not being funny, he's being an asshole. Putting him on the radio so he can tell everyone they should shut up, not him, is just rewarding him for being one and letting other assholes know that it's okay to be an asshole.