I'd say it is strong emphasis on models predictive power, to the exclusion of judging if it improves our understanding of the world. The "shut up" part is more key than the "calculate".

I am not sure if we disagree here or not.

Predictive power has not always trumped understanding as a goal. The original Copernican theory did not work as well as the Ptolemaic model used by astronomers. The Ptolemaic model as it had evolved in the 16th century was extremely complex with many fit parameters and predicted planetary motions relatively well.

All of the models shared the incorrect assumption of uniform circular motion and epicycles, both the Copernican, Tyco Brahe's hybrid system, and the traditional Ptolemaic model which by virtue of the thousands of years of effort invested in it -- it arguably dates back to ancient Sumeria -- actually predicted the motions of Mars and other planets best.

It was only the addition of elliptical orbits with non-uniform motion by Kepler that resulted in the new model surpassing the Ptolemaic model.

In the case of planetary motions, understanding ultimately proved critical. We can predict planetary motions to about 1 in 100,000 accuracy versus about 1 in 100 with the Ptolemaic model of the 16th century.

Understanding always trumps simple accuracy, because it defines new mental models which can tested experimentally.

I don't think it's about low-hanging fruit so much as the difference between analytical understanding/talent and deep creative insight.

Science-as-career has become institutionalised and conservative, and slanted more towards the semi-industrialised production of regular publishable refinements and less towards deep insights.

It's correspondingly less likely that a mind like Einstein's would be able to make equivalent contributions today.

I think Kepler was the epitome of "shut up and calculate". Measure the motion of the planets, come up with detailed formulas describing them. Newton transcended that by identifying simple relations and invariants that unfolded to exactly those equations. I'd argue Newton and Einstein are the only two who have transcended "shut up and calculate". In the latter case we otherwise would have patched in Lorentz transforms and stated "just because" like Kepler. In quantum mechanics, I feel like it's still something on a Kepler level, equations "just because", waiting for a more fundamental understanding.

I would say certainly not. In Nova Astronomia in which Kepler lays out his discovery, one finds chapters and chapters (originally in Latin) of verbal analysis of what is going on. He did not just find a formula that worked blindly. Rather he envisioned an influence -- either magnetism or something similar to magnetism -- which he calls specie (a Latin term used in magic and mysticism) extending out from the Sun guiding the motions of the planets. This was a clear precursor to the concept of a gravitational field.

Reading your post again, I think we agree.

I'd just point that, even tough Schrodinger and de Broglie were pretty much focused on understanding, their contribution to quantum theory was very prediction-based, and not so much understanding based. As I said up there, it's not that they believed that, it is that they only got results when working this way. I took Einstein away from your list, there are always exceptions.

What I think is most interesting is that the XX century got an example of each of those "ways of doing science" working. There was probably a "right tool for the job" effect there, as people certainly weren't trying to create a predictive-only theory.