Absolutely it’s doable. Agreed. Used to beat up the traffic pattern doing touch and goes in a C550, with a departure end turning climb to inside downwind, configure, then come off the abeam, base to final for another T&G. Rinse, repeat. The thing flies akin to a T-37 that has a passenger cabin. A 172 with jet engines, as you accurately describe it. If this guy can’t handle that, then he shouldn’t be in it.
737 is also easily capable of a traffic pattern. Had a go around one time in the -200. Tower wants to hand me off to departure for vectors back, i just ask the other pilot to request departure end closed for a full stop. Nothing requiring any hard maneuvering, just an easy turning climb to the downwind at flaps 5. Configure the rest on downwind, and finish the pattern to a landing. Almost takes no thought.
This guy definitely has many issues, to put it lightly.
