The fundamental obstacle is that we have no conceivable way to produce the energy levels to test the predictions that new theoretical physics would produce. We are like over a dozen orders of magnitude off.
There's a lot of everyday stuff in physics which is unexplained like the particle masses we have.
And a lot of condensed matter physics. Type II superconductivity is a well-known one, but there are a lot of more less well-known ones
The Maxwell conjecture was a conjecture in theoretical physics (though not a particularly important one)