Here's the spec. for a TakeOff Performance Monitor, published in
1987:
sae.org I think that's what we're all asking for? If you have $61 to spare, you can even read it!
I haven't seen the document but I'd assume the problem is a little more complex than you might initially think. However, in these days of GPS and abundant storage/processing power, I'd have thought it would have been possible to construct a device that took as inputs the stabilised N1/EPR from the engines and the flap setting, measured the acceleration (and so determined the mass), then did a quick calculation from knowing (independently) where you were and where the end of the runway was.
If this calculation showed that you wouldn't get airborne in the length available, it would trigger a warning (possibly configuration?). If the warning system was set up so that it would only trigger on recognising a severe performance issue (= impending crash), then there would be much less likelihood of false warnings. The technology is there - certifying such a device is another issue completely...