Oleo,
Power for speed is only practiced on a powered approach,not in the climb. Its purpose is to ensure a constant rate of descent from 500 feet to the landing point.
It is not unlike your box idea i.e dont make excessive changes of attitude, but why accept a box when you want to land at a point. If you fix the landing point on the windscreen, the only variable left is power. The basic assumption is that if you start from the right position, the changes required are minimal.
The practice of descending on the downwind leg is not taught to PPL students in the UK to prevent them from making a low and slow turn onto Final with the risk of a stall and spin. It is primarily designed to keep it safe for the infrequent flyer.