ASR will not help improve efficiency unless you don't care about the mistakes made by ASR (for example, close captioning of real-time audio). Why? Because transcribers will need to listen to audio again to be able to correct the mistakes made by ASR. Basically, once ASR listening to audio and then transcriber listening the audio again to correct mistakes made by ASR. Also, you will increase you cost as you will need costly "editors" to correct the ASR mistakes instead of cheaper "transcribers" to transcribe, reviewing and transcribing requires different skill set.

At one time I invested in a medical transcription business that experimented with voice-to-text technologies but couldn't generate any additional efficiency in transcription by using technology. What worked in improving efficiency was the transcriber's knowledge of medical terminology and medical field, matching the same transcriber with the same speaker as transcriber became acclimated with the nuances and tones of the speaker, and letting transcriber handle only certain type of transcription.

Transcription is a manual operation and Toyota Way is a good way to maximize efficiency.