I read through this whole thread and I didn't see what I think is the primary answer for PADI's insistence on a BC with power inflator. It's the same reason they insist on ditchable weights; surface management. PADI really emphasizes the ability to stay positive at the surface, and for good reasons considering most of what they do is teach certification classes to people with little or no dive experience. I realize BC manufacturers don't certify their products as life jackets, most likely for liability reasons, but that's what they're most often used as for new divers and OW students. PADI cites some statistic like half of diver accidents happen at the surface in their OW classes....I'm not sure of the number, but that's the gist of it.
I personally think that all divers could benefit from doing some diving without a BC in terms of developing good swimming skills, weighting strategies, and breath control. In warm water, with a minimal wetsuit, double hose, and small neutral tank, I've gone on several no BC dives, it's really fun.
To answer your question about what circumstances it's safe to dive without a BC, my opinion is that it's safe as long as you don't need the surface support of a BC, and can swim your rig to the surface without a problem. So this might include shore diving where you can easily swim to shallow water, or boat diving with a float you can hang onto.