Are most machine learning problems the same problem? (NP-hard)
I don't find this a useful or accurate perspective.
It's not true that all NP-hard problems are identical, not even under polynomial-time reductions.  All NP-complete problems can be reduced to each other in polynomial time, but NP-complete is different from NP-hard.
When you see someone say something like &quot;all NP-complete problems are the same problem&quot;, that is an informal slogan that should not be taken too seriously; you need to look at the technical statement behind that and see whether it is relevant to what you care about.  In the context of machine learning, I don't think it's very relevant or useful.
Machine learning is about average-case behavior, not worse-case behavior.  NP-hardness is about worst-case behavior.
In machine learning we focus more on behavior on typical problem cases, rather than worst-case problems.  For example, the no-free-lunch theorem demonstrates that no ML algorithm will work well on all problems.
In machine learning typically we are more interested in understanding their accuracy rather than their running time, and usually we are concerned with concrete performance on concrete tasks and empirical results rather than asymptotic running time or provable guarantees.
For these reasons, the tools built up for NP-completeness and NP-hardness may not add a lot of insight about machine learning.