Re: "Not available in this country"
"If you are traveling, it's not a problem. Your OTP's are exchanged before you travel down under."
One time pads are awesome -- Properly done, it's the only truly unbreakable encryption we have. However, they can only be properly done if you already have a secure means of distributing the pads.
As you note, this is no problem if the parties that want to communicate start off all physically in the same room together, and they have generated in advance enough numbers to cover all the communications that they may want to engage in later (since you should never use the same sequence twice, as Germany found out in WW2 when their inability to generate and distribute enough random numbers later in the war caused them to reuse pads, which led directly to the encryption being broken).
In any other circumstance, though, this key exchange is a very serious weakness. That's the entire problem that PKE was invented to address and is why, even though it isn't technically unbreakable, it is widely used. Any weaknesses inherent in PKE pale (outside of specific and uncommon circumstances) in comparison to the key exchange problem with other methods.