That's not really the case. OTP requires a large amount of perfectly unbiased randomness, implicitly from a hardware randomness source (otherwise what you have is more accurately a stream cipher).
Contrast with deriving a key using cryptographic primitives, which can accept low-quality randomness (as long as there is sufficient entropy), that can be easily and transparently collected.
Yes, in theory OTP requires perfectly uniform uncorrelated random input. However, in practice, you can use a randomness extractor… at which point, yes, we can't prove that someone with unbounded computational power wouldn't be able to crack it. But all known computational power is bounded.
Right. So now you have to figure out how to get a secure RNG into people's hands, so they can create pads. How does that work? Genuinely curious whether there's a reasonable solution.
Devices that produce a trickle of truly random numbers can be produced for a few bucks. They're included in modern CPUs, for example.
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.
