There are many very significant scientific questions that are not understood but our tools are not sufficient to answer them.
At the fundamental physics level, the LHC energies are unlikely to detect the supersymmetric partners of the Standard Model even though we theoreticially know they should be there. This also goes for the unification of gravity forces with the rest of quantum mechanics. Building sufficient tools would cost billions even if there was a public interest in supporting this science.
Chemistry has fractured into many specialty fields including the basis of life, systems chemistry.
Biology is the science that may transcend the other physical sciences in the coming years in terms of new discoveries. The advancements in synthetic biology are approaching the point of originating novel lifeforms from basic nucleotides using computer designed genes. Perhaps the most profound research is in the field of morophogenic programming. This involves identifying the cellular communication structures controlling the growth of a complex organism from a single cell and reprogramming this cell network to regenerate failed organs and systems. This is independent of the genetic DNA code which makes the proteins but does not architect the actual structures. Such technology could eventually extend life for decades or even centuries.
Something like that was my thought as well. We have a lot of specialty STEM schools that are supposed to be directing young people into science and technology, and it doesn't seem likely that political correctness dictates what physicists and chemists do, but it does happen in history that science stagnates when the tools and instruments aren't there for the next generation of experiments and theories.