This is a numbers game, like any other. The probability is that taking off after v1 with engine problems will statistically leave you with the highest chance of getting back on the ground safely. Of course SOPs cannot account for every combination of problems, yes, there may be the odd example of not following the SOP saving someones skin, it would be true to say that in those few seconds after v1 (where you might not be able to tell how bad the problem is) you shouldn't be second guessing the applicability of V1.
If there were to be a paradigm shift in the way pilots were trained ("V1 is a guide, however if you have a hunch you're in trouble, STOP") would this not results in a greater instance of runway overruns? A greater number of accidents? Overruns, incidentally, seem to be painted by SSG as an almost safe incident with the result being only structural damage and a few pax injuries. I was under the impression that fields/roads/housing estates present at the end of runways may result in rupturing of fuel tanks? Not very survivable.