This policy by some operators of empowering the first officer to use the word "STOP" frightens the hell out of me.
In my airline FOs can call stop for a limited number of failures: any fire, engine failure (must be indicated by two parameters), Windshear Ahead warning or Monitor Radar Display warning. In addition, when PF, control difficulty or blocked runway.
Our FOs are well trained and competent. If they are not competent to call stop in the above circumstances then one would have to question their suitability to be pilots.
Our FOs are also allowed to start the engines, handle the the thrust levers, and taxy the aircraft too. They have slightly stricter landing limits than captains.
To waste time pointing out an engine failure or a control problem to a captain and then waiting for him to call stop would seem unnecessary and possibly disastrous.