One-time-pad encryption As we know, intercepted ciphertext created by a one-time pad only reveals the length of the message. That is the only information the attacker can get since this ciphertext is unbreakable without the key. 

I understand that for a file 1GB in size we need a key that is 1GB long. My question is: why is the one-time pad not more widely used in encryption for communications that use a small bandwidth?
One time pads are used in many low bandwidth situations.  However, they suffer from a fundamental problem of key distribution.  It's hard to transmit 1GB of key information.

One time pads are most effective in situations where the trust communication channels are highly asymmetric.  If you can hand deliver your OTP to an individual, positively confirm their identity, and then hand the pad over, then OTP can be quite effective.  In times of war, where you can be physically provided your key material before you travel into the hostile area, this pattern can be very powerful.  In more symmetric situations, transferring the key material securely can be just as difficult as transmitting the material itself!  These symmetric situations are more common on the internet.