But that was never the problem. The problem is, now what? To use this OTP you need to securely deliver pads to everybody you'll ever send a message to. So, OTP is practical for a handful of secret agents who'll receive messages of a few dozen words per year from a single controller, and useless for most of us in the real world.
_This_ problem is why we have public key cryptography.
The only thing that OTP buys you is that you can exchange the pads at your convenience any time before.
With a few GB (a couple bucks in a supermarket will buy a 8GB usb stick) you can communicate in text about 16 thousand books worth of words.
In other words, to deplete the pad you would have to write sixteen thousand books.
I think that's pretty convenient, as far as literally unbreakable encryption goes!
It's just that key-sharing is basically the most complicated and vulnerable part of modern cryptography.