Just a further note on the decision making process as it currently stands.
Pilots are human beings, we are simple creatures who can easily become overloaded with information. We need a simple clear-cut decision making process. At my company (Airbus aircraft) our take-off safety briefing goes something like this:
- Below 100 knots* I will reject the take-off for any abnormality.
- Below V1 I will only reject for an engine failure, a fire, or unsafe condition (to cover things that are obviously unsafe to take into the air like controllability issues).
- At or after V1 I will continue the take-off.
Modern airliners will inhibit unnecessary warnings (“dings”) during the take off roll, so essentially they will only give a warning for something that you need to reject the take-off for. This means that line two can be reduced to “if it swings (engine failure) or dings I will stop”. Simplicity rules.
Note that the decisions making gets more and more simple as speed increases and time to make a decision decreases. Below 100 knots you’ve got time to look at what’s happening and bring the aircraft to a stop in a controlled manner, you can stop for anything. Between 100 knots and V1 a rejected take-off is a more serious matter and the decision is distilled down to just two scenarios with a bit of a lawyer clause to cover unicorn events. After V1 the decision is made, you are going. There may be very rare cases where you could decide to stop but they’re not worth thinking about because they are rainbow unicorn events 
. Adding a complication to what should be the simplest of decisions is not helpful.
There is a magic number in aviation that relates to the chances of an incident of a certain type happening. I can’t remember it and my Googlefoo isn’t working adequately, @mnemosyne might know it or know of something similar. Essentially if the chances of something happening are below a certain amount, that is considered to be ok. There is no need to spend money or writing regulations to mitigate that particular risk. When we head across the ocean and spend periods of time where we are several hours from a suitable airport it’s been calculated that the risk of more than two significant failures is low enough that it’s not worth worrying about.
If we are three hours from an airport and have an uncontained engine failure that punctures the fuselage and causes a depressurisation, that’s ok, but if it also causes a fuel leak, then you’re fucked and ICAO, the FAA, EASA, and all the other regulatory authorities are basically ok with that.
You have to realise that having an engine fall off the wing and cause a fire that causes a failure of a second engine is getting into the we’re-ok-with-that part of the risk equation.
*100 knots is an arbitrary number used to delineate the low speed take-off phase from the high speed take-off phase. Boeing, as I understand it, uses 80 knots. The actual number doesn’t matter,