1. An engine is less likely to fail at lower thrust.
Now, that’s a reason I would have given and it seems obvious but is it actually true of modern (jet) engines? Are there any statistics available to back it up, genuine question? With many piston engines peak mechanical and thermal stress occurs at less than peak power (not that this has anything to do with turbines but it shows that the simple answer is not always the most correct).
2. On the longer runway ASDA for an RTO is less likely to be the limiting factor, so less braking may be required reducing the possibility of a brake/wheel fire or tyre deflation. Again, safety improvement.
With the software we use, adding runway length often results in a lower flap setting (increased speeds) and improved V2 (even more speed). As brake energy is proportional to speed squared, that can be quite significantly more in the event of an RTO.
3. What may conspire to kill you on the day may not actually be the certified standards of engine failure/stop/go scenarios. In fact, none of these should kill you because the aircraft is certified not to. What may kill you is a multiple failure, an error (eg thrust calculation error), a sticking brake, tyre failure, manipulation or handling error, or other event that is not possible to plan for. In that case, having more runway to sort it out may save you.
Agreed. Although I would add that there are many examples of aircraft failing or nearly failing to get airborne from very long runways due to too much thrust reduction, which might not have happened if full thrust or thereabouts was expected to begin with off a much shorter strip.