FWIW, it takes way more than 1 second for the engines to spool up. And an engine not producing sufficient thrust would not doom the plane -- as long as the airplane makes it to V1 (decision speed), it should be able to fly with a single engine failure after that point. And the pilots should already have talked through the takeoff and come up with a go / no-go based on distance: "if we're after this point and we haven't reached V1, we'll abort".
One detail: V1 is the last-chance speed for being able to abort the takeoff within the remaining runway length, but it is predicated on the weight, among other things, being correct. If the airplane is heavier than the figure used in calculating it, you will not be able to stop in time from V1 (you will reach it later and further down the runway, yet need more distance to stop.)
Having said that, a speed-at-distance rule like the one you give here, especially if it was evaluated at a distance before you expect to reach V1, would be perfectly good. There is a rule-of-thumb for small-plane pilots saying you should have reached 80% of the rotation speed before you are halfway down the runway (though that speed is also weight-dependent - as demonstrated in these incidents.) There is a tacit assumption here that your deceleration after choosing to abort will exceed your acceleration up to that point.
True, but the spool up rate and thrust produced during spool up is all predictable.
Basically, I'm saying the plane should have an internal mathematical model of what it expects to happen, and anytime that sufficiently differs from reality, it should trigger an abort - especially if you're still on the ground at the time!
This parameter is displayed on some aircraft, notably French (Mirage 2000 & Rafale) which display the longitudinal acceleration (labelled Jx) in the headup display. Part of the takeoff procedure for the pilot is to confirm the Jx is nominal with regards to the takeoff parameters (loadout, density altitude, etc.).
Hopefully you mean tell the pilots to abort and not start the process itself. What if there's something on the runway or the runway is too short or slick for the plane to decelerate? There's differences between conditions and runways that would have to be accounted for and then you'd have to add a lot more capabilities to the plane's sensors for every other possible issue.
It's often a judgement call when things don't happen quite right and I don't think our technology is anywhere near ready to hand the abort process over to the plane's programming.
