The joke itself is anecdotal, showing that THIS couple has a neurotic wife, and a unresponsive husband.

What? That's not how culture works. Or art, for that matter. It's obviously not supposed to be taken in such a way, but in more of a "Women? Amirite guise?" vein. Because if it was seen as "anecdotal," it wouldn't be relatable and it wouldn't have 474 upvotes (minus fuzzing, I guess).

So is the joke sexist? Sure. To both genders. Men never talk about their feelings to their wife? That's a sexist stereotype!

Yes, that is exactly my point. Furthering jokes like these just enable stereotypes and lead to discrimination against people, because it also normalizes the stereotype! I don't know if you've ever read Faces of the Enemy, but it outlines how iconography is used to dehumanize people. And it is used because it is damn successful. It makes hatred, if not "mere" stereotyping, easy and socially acceptable.

So, if you care about egalitarianism at all you should be fighting against these jokes. People should be as uncomfortable to tell sexist jokes as they are racist jokes (or at least jokes about blacks; jokes against Asian people seem to be fair game these days).

And before you say 'That was my point! No more sexist stereotypes!', it's at this point that I say: You and ElDiablo both pointed out you can't tell people what they can or cannot find funny, but people love to laugh at themselves. This joke is funny because of the GUY'S response. That IS the punchline. I'm willing to bet that many are laughing about this because, as motorcycle enthusiasts, we 'get' that our bikes breaking down would seriously distract us. Again: They guy in this joke is more dysfunctional, and we laugh because we know that about ourselves: Our love for our bikes borders on dysfunction.

Does that make it better, or healthier? This isn't self-deprecating humor. This just makes me feel like it is humor directed towards men who both hold sexist views against women (ie. the whole "lolololol irrational women u so funny"), but also men who have internalized destructive stereotypes.

does then stopping the jokes is only a band-aid solution to a deeper problem.

What makes you say this? It isn't a conclusion to your joke. In wars, for example WWII and the Yugoslav breakup, iconography and jokes and the like were all used to dehumanize the "other" and make them easier to kill. Obviously this isn't nearly as (immediately) serious, at least in the west (I'm thinking of the infanticide in India and China), but if you make these jokes unacceptable it makes it much harder for current views to be as easily held, and it also makes it more difficult for new people to be indoctrinated in these views.

And if there IS a problem, then the rest of us would prefer to laugh it away.

But laughing at a joke like this (ie. accepting it as true in some form, for if you didn't accept it as even a bit true it wouldn't be funny) isn't laughing at the problem. Complaining on r/circlejerk/ or SRS about the discrimination virgin, white neckbeards face is actually laughing at the problem.