Why is the takeoff decision point based only on speed and not time or distance?
Manually checking:

My guess from a human factors perspective, focusing on 2+ things (e.g., speed and time) is harder than one.

Newer aircraft have installed automatic monitoring though. For example for the 787:

This message is inhibited 6 knots before V1.

Or the similar system (supposedly) on the A350. Airbus calls it ACUTE:


  The Airbus Cockpit Universal Thrust Emulator
  (ACUTE) converts the engine control parameter into a
  common Thrust parameter (THR) for all engine types.
  The thrust parameter varies between 0% and 100% in
  all flight conditions.


This would understand a faulty/blocked EPR probe for example.

For inadvertently holding down the brakes (extremely rare occurrence), the brake temp should rise considerably. And with today's glass cockpits, a warning will be easy to spot.



Automatic accurate monitoring of acceleration:

A warning system built to use the accelerometers on board will need to measure the acceleration against flight test data. But not just acceleration, a plane's acceleration on takeoff varies, due to increasing drag and decreasing friction (landing gear decompression).

See this PDF, and this post: Does acceleration increase linearly on a takeoff roll?

An average positive runway slope value used in real life can be down to a runway sloping down, then sloping up at the end of the runway. Some dispatchers note that, others do not need to. But this false value can trip the system.

My point is the variables are immense—even nose heavy acceleration will be different—and would require lots of money to test, verify, test again, then have a system that can monitor all that. I'll bet there will be many false positives.

Add to that when to start measuring it, a pilot pushing TO/GA at 10 knots (ground speed) versus 40. IAS is useless here due to wind.

If the system will allow for big tolerances, then properly trained pilots can notice it much easier. To borrow what Carlo said here, using TLAR (That Looks About Right) is enough.

Let's not forget that there is a speed trend arrow on the airspeed indicator on most of today's airliners:

Green arrow shows what the speed will be in 10 seconds on a Boeing 787.



Coming soon:

For the generic very slow acceleration (as far as I can tell), Honeywell is developing that system as part of their SmartRunway package. (Thanks to fooot for mentioning that.)


  He advanced the throttle to a setting too low for the weight of the aircraft and started the takeoff roll, with distance remaining ticking down on the display. At 80 knots, a yellow box framed the runway and “ACCEL LOW” appeared at the top of the screen. “Caution: acceleration, acceleration,” said a female voice from the simulator setup.




Regarding the method used by the USAF (explained here): it does not work for the big civilian airliners due to the disparity between an empty plane and a fully loaded one (compounded by the environmental variables). A 777-300ER can carry anywhere between say 20 tonnes (fuel for a short hop), and 183 tonnes (payload and fuel).