But, aside from these big problems, many smaller problems are susceptible to experimental investigation. You may not create an Einstein-style paradigm shift by detecting CNO-fusion neutrinos from the sun, observing Higgs decay, improving quantum-dot solar cells, fabricating nanotube rope whose strength approaches that of a single nanotube, understanding the lubricity of BAM well enough to design more similar materials, deriving useful energy from the fission of lithium, making a metamaterial with a higher Young's modulus than diamond with negative-elasticity inclusions, constructing logic gates out of fluid vortices, building a usable hypersonic plasmoid pistol (one that doesn't require explosive flux compression pumping!), building transistors that function at 800 degrees, finding a SHS route to cubic boron nitride, making a 50-tesla magnetic field in the lab, finding a way to construct quantum-dot solar panels that's cheap and scalable enough to undercut poly-Si, confining a particle of gold in a stable minimum of the Casimir potential, or finding a way to fabricate high-quality optics apparatus rapidly out of aluminum foil; but the obstacles to these problems are (or were) mostly not that we don't have any useful hypotheses to test.
In https://news.ycombinator.com/item?id=29144119 I listed a lot of the big unsolved problems in physics, though many would argue that the question of how consciousness arises isn't part of physics. In https://news.ycombinator.com/item?id=29153894 I also listed a lot of recent advances, many of which came from experimental physics. Some of those problems are susceptible to experimental investigation even with the theories we have.
Edit: The problem with physics today is exactly like back then, we have no predictions to test. If someone comes up with a new theory that joins quantum physics with gravity in a way that is consistent with all past experiments, then we can test that. But there is no such theory today, nobody has figured out a way that the domains can work together.