https://en.wikipedia.org/wiki/Cambridge_capital_controversy
It boils down to the question “do we get richer by making more or demanding more” and there are plenty of paradoxes depending on which side you choose (If it’s because we make more, then why did the 2008 recession lead to a persistent step-down in GDP growth? If it’s because we demand more, then why does technological innovation seem to matter so much?).
But ultimately, the best economics is observational and that question isn’t the most relevant to observational economics
"All models are wrong, but some models are useful." I have come to believe this quote is one of the most important things to understand about human knowledge, and certainly anything worth having an "intellectual debate" about. Because the vast majority of debates are actually about models. Losing sight of this is one of the most common ways debates veer off into uselessness (even between otherwise intelligent, thoughtful people).
Economics is really, really hard. We know markets involve billions of people and unknowable forces and chaos theory and irrationality and all sorts of other complicating factors. We know that even our very best economic models are going to be mostly wrong most of the time. Anyone who doesn't accept that is blind, and you should not listen to them. This is true of all the "soft sciences" like sociology, anthropology, and linguistics: they're largely full of B.S., but not because the practitioners are stupid or bad or corrupt, but because it's so tremendously difficult. From a certain point of view, physics and chemistry are way easier, precisely because their phenomena are more predictable and therefore easier to model. I applaud all good-faith efforts in the "soft sciences", even when they produce B.S. -- they are important subjects for humanity to study, and we should all understand accept that they are extremely difficult. In many ways, these subjects are still too complex for humanity to grapple. And the more complex the subject, the more wrong its models are, and the less useful they are. We must be extremely patient with these sciences and not expect giant leaps and perfect models, because humanity is just not there.
There's no problem with the soft sciences being mostly filled with bullshit as humanity tries to improve our understanding of them. The problem is when people ascribe too much importance to that bullshit and pretend that their models are much more widely applicable than they are. It's usually pop-science writers, snake-oil salesmen, and laypeople who are responsible for this, not the scientists themselves.
So while it is extremely important to study economics, we should still not expect too much out of our economic models. They're pretty bad.
Reading this Wikipedia article, the overwhelming felling I'm getting is: this is an internal debate about the specific edge cases of extremely specific economic models. Of course we all ignore it. Because those models are both wrong, and likely not even particularly useful. I'm really glad those debates are happening -- we should constantly strive to improve our models, and debates like this are part of that. But unless you're working on developing those specific economic models, why would you give a shit? Most people ignore the debates between FORTRAN and COBOL too, unless they're particularly interested in the deep specifics of (largely historical) programming languages.
Both Cambridges' models are bullshit. Both of their models are barely helpful for creating effective economic policy, and nearly worthless for any other use. Both of their models are wrong. I can say that with certainty without knowing the specifics of the models. But again: it's tremendously important that we make these bullshit models and have these kinds of debates, because that's exactly how we make slightly-less-bullshit models in the future! So more power to the Cambridges, but you should not think it some intellectual failing of other people to not give a shit about it.