At Sleap in the 1960's, the CFI was a pragmatist who appreciated that what ab initio students need is as many landings as can be squeezed into the hour, and that flying text-book circuits was a waste of time and money. Accordingly, he and the other FIs would take control at 200ft after take-off, fly the shortest possible route to line up on final at 500ft, hand over to the student to do the next touch-and-go, and take over over again at 200ft.
We were the only operator at the airfield, which made that easier. But most regional airports don't have all that many commercial (ie priority) movements during much of the day.
At Sleap in the '60s I flew as often as I could manage with the great Adam Wojda, an ex-RAF Polish FI with little respect for authority. One of my sessions with him was learning how to fly a really square circuit (not needed at Sleap, but elsewhere there were stuffy controllers, eg Sywell) by doing a neat little modified stall turn at each end of the downwind leg. He also taught me to sideslip the Auster from side to side down the final approach; it gave you a better view of where you intended to touch down. Evidently this was common practice in WWII tail-wheel fighters, known as fish-tailing.
Much later in life, I would make my feelings known that the flying club at an airport I worked at was simply defrauding its students by flying ridiculous "Bomber Command" circuits that took anything up to 15 minutes. Their problem was that the FIs didn't know any better. My heart sank every time I saw their Cessna 150s being dragged down a 2-mile approach with flap all the way and lots of power. This still goes on today, and it's wrong.