A headwind would generate an increase in airspeed, so if the system used airspeed it would show an increase in performance. But these are technical issues that can be solved by proper design, not reasons to not bother designing it at all.
You would be measuring sub-knot airspeed at 40 kts. And you're talking about acceleration. Acceleration decreases as the plane gets faster.
This was an area of active development 20 years ago, and you can search for the literature if you don't believe me. There's even a SAE AS on how well it's supposed to work. Once in a while a safety board complains about it, but you simply can't have a good model until you're close to the high speed regime. It's different measuring time to rotation or time to 110 knots, not 50.
Draw another analogy, take a car and floor it. From the time it takes to get from 0 to 30, estimate its top speed. To 15%. With a fat guy in the back, speed bumps, rain and wind.
To mathematically prove it's not going to work, take a state-space model of an accelerating airplane and calculate the observability grammian at low speeds. It's basically the calculation I showed you. It's not that nobody's tried, it's that people have tried and realized it doesn't work until high speeds, and as everybody agrees then one false alarm is going to cause a big problem.