One-time pads need you to have a limited amount of data to encode and a good channel through which to send your one-time pad. However, assuming AES isn't broken by quantum computers (there is no evidence that it is), you could use a relatively small one-time pad to generate keys to encrypt a much bigger bulk of data.

Not the craziest idea in the world, but you still need a very secure physical key distribution medium, which is hard.

Quantum key distribution solves the sharing problem and will arrive sooner, for a certain budget.

I'm not so sure - QKD needs good SNR optical paths from source to destination, so over any real distance it's pretty hard. Physical medium security is just a matter of money today.

There are ideas of satellites doing QKD, but that will fall firmly into the realm of nation-states, which already spend a shit load on physical security.

This is covered in the article. It even links to the exact same page.