Not quite. It is used to nail the correct AOA for the operation, not "as close as possible to critical [stalling] AOA". A properly adjusted stall horn will not normally be sounding at proper short-field approach speed. Stall horns typically sound off 5-10 knots above stall, and best short-field approach speed usually isn't in that range. Further, even if it were that way, the best airspeed for that varies with weight, but the best AoA does not. With an AoA gauge, you don't have to compute the change in speed off the book recommended value for less than max gross weight -- just nail the correct AoA regardless of actual weight.
Further, it will do the same for best range glide speed, best endurance speed, max range cruise, Vy, Vx, etc. Makes it a lot easier to fly the plane for any desired performance parameter.