Close, but no cigar. Most speakwrite programs only work when they are trained to understand the speaking peculiarities of the individual user. Witnesses, OTOH, all speak differently, often with slurred voices, foreign accents, and mumbles. In addition, there are often very many persons whose testimony is being transcribed in any given month, meaning a program can't be trained to catch the unique characteristics of each. Thus, the only machine that can really work is a human being with fully functioning eyes and ears. A court reporter often needs to watch a witness’s lips to understand the witness. Finally, if the court reporter can't understand a witness, the reporter can always ask the witness to repeat his or her testimony.
It’s like medical records (medical transcription). It’s now done on voice recognition, but there are so many doctors from all over the world with many different accents and inflections that it still takes a person to edit the medical record. It’s scary what the program “thinks” it hears, especially when it comes to drugs and dosages.