Actually, I can't think of any of our instructors or DiveCon's who don't use the integrated power inflator and all of the with newer equipment (myself included) use the Seaquest Air Source. I do not carry an octo. As we teach to hand off the primary in an OOA situation, I am breathing off the Air Source anyways if I am donating. One of the many reasons that we teach this is precisely because not everybody uses the same back-up air supplies anymore, but most everybody knows about their own secondary. So, you don't have to think about handing off your primary and going to your own secondary in this situation. But that is a another whole debate.
The advantages of the integrated to me are simple. I can't think of the number of times that I have noted new divers not clipping their octopus to their gear tightly enough or they lost their clip. Now it is in the dirt and/or not readily at hand. Not only is it likely clogged with dirt, it is creating a silty mess on the bottom. I know where my air source is because I have been controlling my bouyancy with it.
To the people that dive with the long hose and bungie necklace... Well obviously that is the way that I dive in doubles, but we try not to confuse students and new divers with different configurations and seven foot hoses on the primary definitely count as a "different" configuration. So, when I am assisting with class or participating in store dives, I am a little limited in my configuration. So, I find this to be the policy for me. But I have dove with a guy who used that in his recreational gear and I liked the idea.