For weddings, I use full manual exclusively. I've been tempted to use aperture priority a few times outdoors, in wildly varying light, but my manual shooting is getting better as I learn to constantly monitor the meter and histograms.
I'm not saying the "semi-automatic" modes aren't good or that they shouldn't be used, but in most wedding photography (in my experience) you need absolute control over the camera - any guessing the camera has to do is an opportunity for the camera to get it wrong. If you're in a setting where you can trust the automatic settings, or at least you can check on the automatic settings and adjust them and take the shot again, then they are fantastic to use. If you're in a situation where the photo has to be as good as possible the first time with no time to retry, then learning to wield the camera in full manual is the way to go.
I haven't even used the Auto ISO feature on the 5D3 yet. I know I can restrict it to a specific range of values, but I think that I should be able to set the aperture, shutter speed, ISO, focus, framing, and composition at the same time. It's exhausting and sometimes daunting, but when it's done right, it's the best way to consistently get great photos.
I'm with you. And I don't know why people complain about the auto ISO so much, because I don't want it at all, so I don't care how it works. It was terrible when one time a new camera (Nikon D90) kept changing the ISO in the manual mode. I hate that.
Like you said, using manual exposure can actually make me work faster. Imagine that I am taking promo photos of classes in a school (this morning's assignment). I set my exposure, and take a picture of the class, and then turn to take a picture of the teacher who is backed by a large window.
With any auto setting, I'd get blackness then and scurry for 15 seconds trying to fix things up with exposure compensation and all that.
With manual I get the perfect shot without changing anything, and the extra brightness behind the teacher just adds a natural backlit effect and hair halo that I couldn't have done better even with all my lights and flashes.
I only use auto modes once in a rare while in controlled lighting settings (ha, ha, this is the exact opposite of intuition) that vary distinctly from one another. Any wild or difficult lighting environment calls for manual exposure all the way, and definitely no auto ISO.