Why then would you have balanced connections if you don't have a fully balanced amp. Just a convenience?
Yes. It is just another way to connect the amp basically, for convenience. One possible advantage is if you need the higher voltage gain that balanced circuits can offer (coming from your balanced preamp or possibly a balanced DAC with volume control). It is rare that this additional gain is necessary. Maybe where very long cable runs are used, this can be helpful. Something to note, however, is that your whole system needs to be balanced in order to take advantage of the noise rejection that a balanced system can provide. I know there are caveats to this that involve transformers or autoformers in the chain, but that's another topic. I'm sure it has been talked about here on AC before.
And thanks for the clarification James, regarding Bryston's models and the circuitry as one goes up the line.