Personally, I think that asynchronous communication is more efficient is a fallacy. In a verbal, synchronous conversation (a phone call), you can communicate extremely efficiently. Misunderstandings or doubts are detected and clarified instantly. On the other hand, finding a moment to listen to a voice message, listening to it, responding later etc. seems to take _much_ more time in total.
This is of course highly subjective. You might prefer the ability to choose the most suitable moments for communicating over communicating efficiently. My impression is, however, that the asynchronous type of conversation just stresses people out because the initial illusion of "just a quick message" turns into an endless back and forth of clarifications. I cannot imagine a meaningful communication on any level that does not require any kind of clarifying question, queries etc.; be it even just for expressing empathy or confirmation.
I wonder if there is any linguistic research on verbal asynchronous communication to make the matter less subjective.