I've yet to see a VALID argument against using the AIR II or any similar system.
Then you have not paid attention at all.
The non standard inflator hose is clearly a good argument against it (I did see at least one post on SB where someone had a hassle on vacation because it broke and it was practically impossible to find a replacement).
It clearly makes managing buoyancy while using it for breathing more complicated. You are trying to do two thins at once with one item. Doesn't mean it can't be done, but it will be harder and it will be different than how you normally do it, which can't be good in an emergency.
I don't know how it attaches to the BC so I am not sure about rinsing it and servicing it and such. I do know that if my BC has a problem, I can rent a BC and use my regs or vice versa. With the integrated, probably not because you have tied your reg setup to your BC setup. That is quite the drop in flexibility.
Whether being "non standard" in terms of common equipment, well that's debatable and the BP/W guys are already different there, as are people trained on older equipment too so I won't count that as a negative, although some people legitimately could.
And does eliminating one hose really justify all that crap? I would much rather have two identical performance second stages. One function per item so it can be the best item possible for the job. You don' use your dive light as a hammer do you? I am sure someone could make it have a nice solid case so you could. Not that you are likely to need a hammer diving.
So there are plenty of valid arguments against them. On the other hand I have yet to see any valid argument FOR the existence of integrated seconds.