In physics it just recently became mainstream to try experimenting with/incorporating ML into thesis projects. Most stuff ive seen it used for is signal processing related. An example might be particle track reconstruction in a time projection chamber with ML instead of a hough transform. I think it's inevitable that these methods will grow in application, but the two biggest problems right now in my opinion are reproducability and quantification of uncertainties. It's much easier to believe someone's stated uncertainties when you can see the analytic functions they were propagated through. There are ways to kindof work around this, but in my mind those two points are the main things holding back ML from broader applications in science. The article talks about ML tools closer to proof assistants / tools for experimentally driven mathematics. Less of a problem in that domain since the ML model only need make an interesting conjecture which can then be examined the traditional way.
I agree with you on UQ. For example, I have seen a couple of talks in my field of neutron scattering, where people are using denoising autoencooders to remove artifacts and fit data. It's also clear that no one has any idea how this effects the uncertainties on parameters for models that are fit on the denoised data, much less what happens if the models are not appropriate for the data.
I think reproducibility can be tackled--at least some journals (shameless plug--I'm a lowly associate editor on science advance) are strongly encouraging people include data/code with publications. I have reviewed papers in Nature Comput. Materials where people have included data/jupyter notebooks (not perfect, but a very good start). It would be great if funding agencies started adding more teeth to requirements on data sharing. However, many more groups are putting their code on Github.
