This thread is fascinating.
I learned to dive before modern BCs with power inflators were standard. In fact, I saw none of them around at the time. We all learned to mouth inflate our BCs when needed. We also learned to be neutral at 15-20' so we were not that negative on the bottom. None of this is a big deal. It's just how it was then.
Fast forwarding to today, power inflators reduce task loading, primarily on descent for a well-weighted diver, but to some extent during the dive when lung volume is not sufficient to maintain depth control with comfort. There's a lot to be said for reducing task loading. There are many fewer steps involved in pushing a button than the process of removing a reg, transferring one's mouth to the BC hose, pushing a different button, partially exhaling into the BC, switching back to the reg, and clearing it. Add some problems to manage while you this, and you have the potential for a larger problem to develop.
All that said, I would not hesitate to jump in the water without a power inflator for a recreational dive again. I have, too, when I wound up grabbing the wrong reg for a dive some time back. It's how I learned, and it's automatic. The biggest difference was my descent speed--lots slower than my usual plummet to the bottom, so I had time to add air to the wing. I've also had a runaway inflator, disconnected it, and continued the dive without incident. This stuff takes some practice and experience, but it's just not that hard.
However, my inflator hoses are all installed (exceptions aside), and connected at the start of a dive. Power inflators add less risk than task loading in my opinion, and they're awfully convenient. I prefer to dive with them rather than without them.