I am a pilot and was a partner in an earlier, but very similar, version of that airplane for about a dozen years. While it’s true that the aircraft flight manual (a 50 cent term for the owner’s manual) doesn’t require the use of carb heat when reducing power to idle, most instructors I know teach the use of carb heat when closing the throttle. We always used carb heat when reducing power because we were taught that it was advisable, whether the book required it or not.
I think every instructor I’ve ever flown with has been both an agricultural pilot and an aircraft mechanic. Those types tend to teach people to fly in the real world which is a place where common sense suggests a belt and suspenders approach might be advisable regardless of what the book says. The late Ernie Gann, a WW II transport pilot who made his experiences the basis for a string of aviation-themed best selling novels, wrote that “Rulebooks are made of paper. They will not cushion the sudden meeting of metal and stone”.
So, yeah. The guy who ended up in the tree might have made it to his karate lesson on time if he’d been trained differently.