A one-time pad XORed with a message doesn't provide integrity, and therefore can't reliably secure an arbitrary protocol. An active attacker can easily flip any bit in the message. An easy example would be flipping a debug bit (presumably it started off 0) so that the server responds in plain text. We could blame this weakness on the protocol, but the point is that without message integrity we do not have a solid abstraction to build on top of. Referencing OTPs as unbreakable obscures this and several other problems that modern public key cryptography actually solves.

One-time pads (and all symmetric crypto) can never be user friendly - every pair of parties looking to communicate has to meet in person and exchange keys. Pop references to OTPs create false intuitions that real encryption takes significant work to exchange large eys, only secures preexisting links, and is only ever done by those with super serious secrets (spies, children in treehouses, spies, etc).

I also didn't mention the hardware random number generator required to use it properly. Getting a hardware RNG for each machine on the internet is probably more difficult than implementing authentication with OTP. But I did say it was a horrible idea for internet traffic, didn't I? =)

Give me a cryptosystem, and i'll give you a reason nobody should ever use it.