What I'm trying to understand is whether the (relatively new) feasibility of interactive video channels allows for building roughly the same level of trust as would be provided by in-person key exchange. I'm basing this on the understanding, possibly incorrect, that encryption with a public key allows for creating a secure communication channel, but not necessarily a trusted one. The hypothesis is that the capability to conduct interactive video provides a way to verify identity and establish trust at roughly the same level as would be provided by in-person exchange (again, assuming 1-1 trust, and excluding TLA threat models).
Example: Alice wants to video chat with Bob to exchange the secret key and verify identity. Mallory sets up a MITM attack, and gives her own public key to both Alice and Bob. Alice and Bob think they are securely talking with each other, but they are actually securely talking with Mal, who decrypts the video, watches it, then forwards it on to the other person.
This is why you can't have a secure communication channel without trust; you don't know if your secure communication is being intercepted, read, and then passed on.
By transmitting your OTP it is no stronger than the method used to protect it in transport, so if that transport method is secure enough to guarantee the security of the OTP, why not simply use that method for everything and forget about the OTP?