Theoretical physics for better batteries?
You suggested correctly that producing better batteries (in terms of their capacity and cycle life) is more of an engineering problem than a theoretical physics one. Still, it's useful to understand where the faults of existing batteries come from.
The sources of bad performance for existing batteries are:
defects in electrode composition
loss of electric contact between electrode parts
side reactions at the interface between the electrode and the electrolyte
Basically, it boils down to a simple fact that we cannot precisely control where the atoms of the battery materials are located. If we could, battery scientists would come up with an optimal electrode and electrolyte material, optimal distribution of defects and dopants in them, optimal structure and shape of their assembly, and optimal interface between the electrode and the electrolyte.
The term for the idea is atomically precise manufacturing, and researchers have been working towards it, either by looking at self-assembling systems or by upgrading existing scanning probe microscopes to move individual atoms. There's a number of works on battery self-assembly (1, 2), material creation with biological vectors and atomic layer deposition. In particular, atomic layer deposition is an obviously physical approach to atomically precise manufacturing. It is painfully slow, but it may work fine enough to produce thin film batteries, with the thicknesses of electrodes and electrolyte layer in the range of several hundred nanometers. These are suitable for thin-film all-solid-state batteries.
I haven't found any evidence that atomically precise manufacturing has been researched for molten salt batteries. There is some traction that I have found outside of my usual lithium-ion interests: there's a need to create atomically precise arrays of nanopores for membranes to be installed in fuel cells, and redox flow batteries apparently need atomically reproducible molecular clusters to be used in catholytes.
I don't know how the future atomically precise manufacturing technology is going to work, but the tech we have now -- self-assembly, bio-inspired and ALD -- will likely be the precursors for the upcoming new tech.
Room temperature superconductors for SMES, superconducting magnetic energy storage, would be nice. They'd also make an international power grid practical. Such a grid would reduce the need for the storage systems that wind & solar power systems require.