So called powerbacks are done, but usually on older aircraft (DC-9) with the eingines on the tail and on turbo props.
Yep, that is correct. I used to travel a lot by commercial airlines in the late 80s and early 90s and actually got to experience one of these as a passenger first hand. The aircraft was an MD80 and we were parked at a gate at Rochester, NY. I recall hearing the engines spool way up, feel the airplane go backwards, and thinking, "wow, this airplane has a reverse gear."
After reading about this I discovered that, if the airport allows this type of pushback, the airline would limit this to tail-mounted engine aircraft primarily to reduce the risk of the engine ingesting apron-based debris.