As I understand key exchange, two parties can agree on a fixed number of secret bits in the presence of a listening adversary. That set of bits forms a cryptographic key which is then used to encrypt data using a standard cryptographic algorithm. And that key is repetitively used over and over, perhaps for an AES session.
What if instead of a key for cryptographic algorithms, a one time key was exchanged for use with a one time pad construct? My system would then exchange another pad for the next message. Could you realistically securely exchange 1280 bits /160 bytes for a Twitter length message?
Note. A true random number generator is available.
EDIT. From initial comments, it seems that the security of the OTP key would be contingent on the security of the key exchange mechanism, say Diffie-Hellman, RSA or similar. So I guess a fundamental part of my cunning scheme would be the ability to use a key exchange mechanism that provided > (160*8) bits of security. Wouldn't that then mean the security proof of the OTP was still maintained? This is a theoretical exercise, so performance is not a consideration (unless we're talking of geological timescales that make it de facto impossible). Could it be done for example as one message per 24 hrs using a modern desktop machine? An SOE agent might only send one message per week in WW2. Just some temporal context.