Very large models trained with sgd variants don't tend to over fit, especially when using few epochs. See double descent.
The coding/math breakthroughs were caused by training models on the subset of their own outputs which pass a verifier, see reinforcement learning from verified rewards.
More data or parameters can break double descent; it's not a magic free ride, e.g.,
https://arxiv.org/pdf/1912.02292
There's plenty more. Read Google scholar
This is what I thought a year ago, too. But how does it explain what has happened since?
That's the historical wisdom, but there are reasons to believe the opposite: that past a certain point more parameters are always better. Basically, that overfitting don't matter, because a large enough model will memorize and build the general solution simultaneously. Then weight decay and SGD noise encourage forgetting of the memorized solution so the general solution takes over.
https://youtu.be/lKoJJxjUfdw is a really excellent lecture that changed how I think about it.
And we’ve consumed pretty much all the data, and that part is getting harder as data is now expensive, Balkanized by owners, litigated and charged for. Couple that with model collapse as models eat their own output (not solved for any models, despite more than a decade of the problem), and add that lots of previously human curated datasets (stack overflow style), and it very well may be the models are not getting much better.