It's just not possible to do it accurately.
I'm no performance guru, but I think we could do it accurately. Why have the military persisted with timing take-offs if it is such a difficult thing to get right?
Surely there could be a chart for your a/c type and engine configuration, down the Y axis is the N1 %, across the X axis is the weight, where they meet is the maximum time to 100kts.
Question for the performance types; how would the actual ambient temp be taken into account with something like this? Could you have bands of say "0-10degrees" 11-20 degrees, and 21-30 degrees, or would that be far too course?
Here is how I imagine it working; if for example you put the data into the laptop and it came out and said max time to 100kts is 35 seconds. You then trundle out to the runway and roll, at 35secs you notice you are only at 98kts, either abort or TOGA and off you go, if you get to 35secs and you are at 85 kts...abort.
I am looking forward to being corrected and having the weak points of this method pointed out as it will help me learn
