The word 'should' in the definition above is there because the V1 go decision only relates to either a single power unit failure without safety margins or an all power units take-off with margins. It does not cater for either a multiple power unit failure or, perhaps obviously, a structural failure or fire. Using 'should' leaves it open to the pilot to reject above V1 in either of these events and accept a probable overrun.
While this may be arguably correct whilst sitting in the comfort of one's own living room it does tend to go wrong in practice. There have been several incidents where a surge has been misinterpreted as a structural failure and a completely uneccessary high speed abort has been called, above V1, leading in at least one instance to loss of life. I think 'should' ought be replaced by 'must'. In the case of the high speed abort the chances of getting it wrong are much higher than the chances of getting it right.
I do agree with FFP, whatever is done must be in line with the SOPs. If you don't like it - change the SOPs.