Securing the nut with a high-strength grade of Loctite will validate whether or not the tapered square bore can be used for any length of time.
If the nut holds and the crank doesn't move back and forth on the spindle noticeably, it may last a long time.
For harder usage, the arm should be replaced.
I would secure the crank nut to normal torque, then stress the assembly by having the rider stand on the pedals while stationary, rotating the cranks 180-degrees and repeating before torqueing the nut again, and before the Loctite in the nut threads hardens. Perhaps with the arm getting "worked" onto the spindle and re-torqued, the movement that loosens the nut can be eliminated.