"Quantum Key Distribution" in no way implies the key is shorter than the message. It actually needs to be longer to allow for error correction, authentication, and privacy amplification (i.e. to compensate for noise that could be attributed to an attack). A one time pad, or vernam cipher, is commonly used in commercial QKD systems. It's not snake-oil. Please google it. It's dead simple to understand and almost as easy to understand why it's impossible to break if used properly. As I pointed out, it's the gold-standard for paranoid government agencies even without QKD, ergo spooks with suitcases on planes.
As for attacks on ECDH, look up Shor's algorithm. That particular algorithm needs a quantum computer to run, but there is no existing proof showing that it is impossible to find one that would run efficiently on a classical computer. Again, the nature of classical communications means that encrypted messages may be copied and archived, so that vulnerabilities found in the future can compromise messages you send today. Maybe nobody will ever manage to crack ECDH, but maybe they will. It's a gamble. Quantum communications cannot be copied and archived so QKD must be broken at the time of transmission or the message is safe for all time. That's the big difference.
Again, I'm not suggesting ECDH isn't fine for most normal people's day-to-day needs. We're talking about secrets that need to be kept for generations that you simply don't want to gamble on.
As for attacks on ECDH, look up Shor's algorithm. That particular algorithm needs a quantum computer to run, but there is no existing proof showing that it is impossible to find one that would run efficiently on a classical computer. Again, the nature of classical communications means that encrypted messages may be copied and archived, so that vulnerabilities found in the future can compromise messages you send today. Maybe nobody will ever manage to crack ECDH, but maybe they will. It's a gamble. Quantum communications cannot be copied and archived so QKD must be broken at the time of transmission or the message is safe for all time. That's the big difference.
Again, I'm not suggesting ECDH isn't fine for most normal people's day-to-day needs. We're talking about secrets that need to be kept for generations that you simply don't want to gamble on.