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
Magnetic formation flying
Magnetically inflated cable
Light sails and beamed propulsion
Advanced magsails. Able to be ground launched if current densities could go up about 100-1000 times from the best available now.
More on magsails
PDF on magsails
Antimatter storage and harvesting work could eventually lead to the large scale creation of artificial mini-magnetospheres to allow antimatter to be created and collected.