For example, a rocket landing on moon looks incredible. But I don’t think physicists would consider moon landing notable progress.
So, with data and compute you could do applications.
The range is literally from discovering that unit tests are good in software to discovering the Van Allen belts to learning about the geology and history of the Moon from the rocks that we brought back.
Could we have learned more science by doing something else with the money? Of course. But it is a dramatic overstatement to say that the Apollo program didn't "constitute any progress scientifically."
If you don’t believe an anonymous person here, see what prominent physicists say clearly on this topic, e.g., Steven Weinberg.
This is not to dismiss experimental research which is quite important, but to distinguish (experimental or theoretical) science from product development.
In https://www.thespacereview.com/article/1037/1 you'll find that he is very critical of manned spaceflight in general, but about Apollo he says, "No, at the time of Apollo, the astronauts did do some useful things. They brought back Lunar samples. They placed a laser reflector on the Moon that has been used ever since to monitor the motion of the Moon with incredible accuracy."
Earlier in the same interview he criticized NASA for canceling Apollo 18 and 19 because he wanted the science that would have been done, to be done.
I guess he didn't say what you thought he said.
That said, his criticism of NASA's efforts with manned flight isn't because he doesn't think that it is useless to go to the moon. It is because it takes a lot of work to get humans there, and robots can do the job much more safely and cheaper. Which also explains why he thought Apollo was useful. At the time the technology of robotics was much worse so humans were the only way to do the job.
If I recall correctly, an interviewer asks him about the scientific impact of landing on moon. He says, “it was there, but it not that great“ and “I think it was money spent on public amusement, and from all money spent on public amusement this money was best spent”
I am not pushing this view; just a relevant comment.
— update, exact statement
I think this was not money spent on science. It was money spent on an extremely important aspect of technology, and it was money spent on public amusement. And from all money spent on public amusement this chunk of money was best spent. [The scientific value], it was there but it was not very great.
He mentions one area, but then says, “but actually that could have been done much cheaper using unmanned robots”
I agree costs are issue here; money that could have been better spent.
Those were useful things that could have been done by unmanned rockets, but in those days, the state of the art in computers and robotics was not what it is now.
The whole "the state of the art" bit I understand as saying that with modern computers and robotics, unmanned vehicles could have done the job. But they didn't have advanced enough computers and robotics at the time.