The 2 second acceleration post V1 is not time for making a decision it is for establishing the required deceleration. Remember that in many aircraft closing the throttles will not immediately stop the acceleration.
Other issues involve V1 minimum. If V1 is at V1 minimum, does the "identify problem and then PIC make decision by V1" not in effect move the speed at which a failure occurs and GO choice is made somewhat below V1 mini? Will the aircraft get airborne in the distance with such a low GO speed?
What about VmcG. FO is PF. With a most critical engine failure situation (in respect of VmcG) and minimum runway width, is there time for the FO to call the problem, the captain to call stop and the throttles to be closed before the aircraft departs off the side?
If the a/c is certifed for 2 crew. Making the stop call a captain's only call means that for the take-off the aircraft is single crew.
The best one however, is explained by using the unfortunate accident at LFPG some time back where a SD360 infringed and was struck by a departing aircraft to describe a potential situation.
Think about the situation with your SOP's while sitting in the cockpit of the departing aircraft involved;
One of the reasons for stopping is "Danger" eg runway infringement.
Aircraft is rolling.
At 105Kt, FO can see- aircraft infringing on the left, well down the runway. What words are they going to use?
They are going to say "DANGER"
PIC is going to say "where" because they have no idea of what is causing the danger. If they did, they would already be stopping.
Now give me the words that in .001 of a second or less explain to the PIC why they have to stop ASAP!!!!!!
OR;
Call STOP STOP
If the PIC will automatically call STOP when FO calls DANGER then why not have the FO call STOP in the fiorst place.
If the PIC will not automatically stop, then the stop will often be started too late to avert disaster.
I think that many have become confused with the big difference between having final responsibility and making a call.
If the PIC is 100% aware of the reason for calling STOP they can override that call. However, how often will the PIC be 100% sure that the call is in error. With such a small amount of time available, A well practiced, well briefed well understood "either pilot can call stop the PIC can override the call" reduces the chance of over-run / failure to get airborne in the distance available / failure to clear obstacles after a late rotation.