As I understand, quantum key distribution cannot be beaten by classical equivalents and they're only good or better because our current quantum computers kinda suck. So the major use case at the moment is proving the tech and developing the infrastructure. The "killer app" of the quantum internet in my mind is as simple as just sending qbits around. Currently every network call involves an observation that collapses the system wavefunction. If you're looking to actually network quantum devices (say, to run distributed quantum computations) then you need quantum infrastructure.