I was going to shut up, but I just can't. This is addressed to no one in particular, but to some of the arguments which have been presented here.
Every procedure, whether designed by the manufacturer or your company, is based on the assumption that a conscious mind operates your brain, and that said mind is capable of understanding and reacting to situations correctly, and making optimal if not the best decisions to give everyone on board the best chances of making it in one piece. If that weren't the case, there would be no pilots.
This whole "go-minded" stuff was not caused by horrible takeoff overrun accidents that killed everyone on board. Yes, people have tragically died in overruns (mostly on landing) and it is not something to take lightly. However, you have 1000 times more chances of dying in a LOC accident while in the air. The actual origins of these procedures are the following: X, Y, Z aviation safety people examined a series of aborted takeoff above V1 incidents (many not resulting in overruns mind you!) and figured out that most of these were perfectly flyable aircraft, and that the takeoff was aborted for some insufficient reason that in the heat of the moment seemed critical to the crew. Conclusion: there is statistically very rarely a valid reason to reject the takeoff after V1, so it makes sense numbers-wise to "force" pilots to press ahead, because much more people risk to lose their lives if we continue to allow these frivolous rejected takeoffs than the 200 lives we're going to save when once in a blue moon there is actually a valid reason to attempt to stop. Or, more cynically, it could be about tyre costs. Realistically, it's probably a bit of both.
Let's take an example where the runway is too short to stop once you've passed V1 and the overrun is guaranteed - which again is not always the case. Now think about it. What offers your passengers the best chance of survival? Driving into the forest at the end of the runway while slowing down? Or nosebombing the same forest from the air because you took off with your wing on fire like a dumbass? And it doesn't even have to be something as dramatic as a fire chewing off bits of airfoil. Anything that would cause an aircraft to refuse to fly is a great reason to stop, no matter the speed. Same if you suspect possible imminent structural failure (wing on fire example). For the life of me, I can't figure out why you would try to power your way through that.
Obstacles at the end of the runway and to the sides are a concern, of course, but you should already be aware of these things before you even report for duty. It is your job to know the aerodrome and have plans in case something goes wrong. Where are the obstacles in case of an overrun? Where can I go? If I have a dual engine failure, where can I go? If I'm already in the air, where can I put her down to give us the best chances? If you're thinking about these things during a takeoff run, you are late. This is no time to discover the layout of the airport. The homework should have been ready from before.
Making the correct decision within seconds is what saves lives or elevates them from this earthly plane in a violent manner. And despite what you might think, there is no procedures and no checklist for decision-making. That burden lies squarely on your shoulders. Try to get used to it.