The canards on the SU-37 supply additional pitch control when operating at extreme angles of attack. In much of the maneuvers on the tape the wing is fully stalled in a normal sense, and the jet is deriving lift from the flat "plate" of the bottom of the aircraft and wings against the relative wind. That, and riding on 50,000 pounds of thrust from the engines. I don't think a stunt plane would look very impressive if maneuvered with the wing fully stalled, and the power required would be *way* beyond what we get with stunt motors.
Our present wings give us plenty of lift without outrageous pitch excursions.
The gyrations of the SU look cool but would be near suicidal in a dogfight. You *might* dodge one missile, you might be able to get your nose on the other guy for a quick guns shot or let loose an IR missile of your own, but you'd have killed your energy (airspeed) and be essentially frozen in space while the other guys would maneuver on you and blast you from the sky. Thats assuming you lived long enough in your non-stealthy fighter to get into a visual turning fight anyway. Most likely an AMRAAM would glide in on you unawares and disintegrate you before you knew the fight was on.....
Steve