There have been various proposals about limiting winch current via a series resistor, but nobody has mentioned directly governing line tension. It is certainly possible to devise a gizmo that would measure line tension, average it over some desired interval, and limit current flow to the winch so that line tension would be capped at some pre-determined amount. Commercial tension meters are common in industrial uses, and it would be straightforward to adapt their design to this purpose.
If you broke the line while using this scheme, it definitely wouldn't be your fault, and you'd get a relaunch. Whether the pilot pulsed or not, the equipment wouldn't be overloaded. Every contest would provide identical launching power, and plane designers would know exactly what parameters to use in trying to optimize the plane's performance.