By getting superconducting theory right (or making enough progress from theory and better experiment), we could guide material design of room temperature superconductors, higher current density material, better electronics, better power grid, possible magnetically ground launched space craft.
Room-temperature superconductors would be an important milestone on the path to complete mastery (within the actual limits of physics) of information, light, energy, magnetism, and matter. (ILEMM control)
What seems doable with far greater mastery of ILEMM:
Large scale Quantum computers (millions of qubits)
Large scale space structures for solar energy collection and propulsion