Lawyers who become politicians often do so because they suck at the practice of law. An experienced and competent trial lawyer would structure the Q & A along the lines that you suggest. In all fairness, however, an effective cross-examination takes time to develop, and 5 minutes, 30 minutes, and even 60 minutes may not be enough time to score points.
It also helps to be allowed to challenge an answer in real time, not an hour later.
Agree. But if 2 or 3 people coordinated the questioning, they could lay it out over a few sessions, with a couple of gotchas in there separated by time to see if the witness contradicts themselves?