Distance/time check has certain practical difficulties, particularly at night which is most of our ops.
And think about this: even a distance/time check would have to be something calculated for each takeoff to account for weight/rwy etc etc. The key word is "calculated". It would be subject to the same input error.
V1-time should not be too difficult though. It must be used in the V1 calculation already, because that's how you know how much runway is used to get to V1 therefore how much is left to stop - it just isn't an output I guess.
If the input data is incorrect, yes it will be in error but that error is exactly what flags an incorrect weight. Instead of monitoring only V1, you monitor V1 and time - if time occurs first, you abort the takeoff. If this happens you know:
- you are below V1 and
- you have have more runway ahead of you than you would have had at V1, because you have been moving more slowly than planned
This wouldn't pick up an error in the runway length however. It also wouldn't flag an incorrect heavier weight being entered, although I imagine that wouldn't be likely to be catastrophic.