PPLs should be happy to do steep turns, slow flight, high speed flight if they want to. And training to the corners of the envelope (but clearly, not beyond, that's test pilot territory and requires some very very specialist training) should be a normal part of PPL training.
Agreed for "happily leaving the middle of the flight envelope", the steep turns and slow flight (and stall/incipient stall), not so sure for the high speed and envelope corners part. Depending on under which circumstances and how it is presented, I somehow feel that being made to feel comfortable at the high-speed/high-g edges of the flight envelope might blur the risk of exceeding the remaining narrow margin into "test pilot territory", not only at one's one potential peril but also for the next users of the airplane (but maybe,
not being an engineer, I am just overly leery of structural issues).