As far as I know, Bryston is using a standard HDMI switching board. It might be custom-made to their specification though but the receiver hardware is the same nonetheless. These are usually 4 input boards so that's why you have 4 HDMI inputs on the BDA-3.
I agree that BDA-3 has too few S/PDIF inputs.
As for theoretical advantages and disadvantages of different digital interfaces, their performance is highly dependent on implementation. I should also point out that optocal systems should have the best possible digital transmission but as you know, this is not always the case. Many, many years ago, Denon invested in a technology they called "optical class A". It brought the company to it's knees because it took so many years and extraordinary resources, both technical and financial, to develop it. Finally, the technology along with all the patents were sold to AT&T to save the company from going under. This is what allowed AT&T to grow so much. But that's a story for some other time.
Not all opto input receivers are created equally to say the least. Bryston is using some very fine ones. They lock immediately onto the incoming signal, they tolerate all kinds of optical cables and measured jitter is almost as low as on it's coaxial inputs. It doesn't get much better than that so there is no reason why they shouldn't be used. In all honesty, with digital TV boxes that providers usually give you, you are way better off with optical connection because when those things fail (and that is almost a certainty), you're avoiding the risk of damaging the input receiver of the DAC which would otherwise occur with coaxial connection. It has been known to happen and there are several posts about it on AC alone.