Hm, sorry my friend, but you are wrong here.
F=m*a, remember?
So, acceleration of the car is proportional to the force it gets from the torque at the driving wheels.
Now, torque at the wheels is related to the engine/transmission gear combo rather than the engine torque alone, but still, it is the torque that does the job, not power.
As you've correctly pointed out the "F" in the "F=m*a" you just quoted is the traction at the driving wheels. And you've also correctly pointed out that the torque at the wheels is not the same as engine torque, because engine torque does not matter once power is transmitted through the transmission.
A quick thought experiment: let's say we have a big engine that has 400 Nm of torque at 3000rpm and a small engine that has 200 Nm of torque at 6000rpm, so both of them have a peak power of 125 kW. Now we gear the transmission such that both cars (also assuming same weight) reach 60mph at their peak torque output. Such a setup will ensure both cars accelerate to 60mph at the same time. Why? Because remember KE=1/2*m*v^2, and t=KE/P. Both cars will hit the same kinetic energy, while having the same amount of power, so it will take the same amount of time for the two engines to impart the kinetic energy onto the cars. You can apply the same simulation to a tank engine with 2000 Nm of torque at 600rpm or a go-kart engine with 100 Nm of torque at 12000rpm. The acceleration figure will not change, because the power is the same.
Now in real world we can't assume all engines have similar
torque curve. The aforementioned "big engine" will generally perform better at normal driving rpms (1500-2500) so a driver gets that power very easily, while the "small engine" will require regular downshifting to, say, pass a car on the highway. That's why people say they "feel the torque" when they press down the gas pedal on a powerful car. But it's not because their engine has more torque, but because their engine has more
power at the rpm they are requesting. Modern turbocharged cars have high low-end torque so they can be more efficient; it is a good solution to have both efficiency and power. The similar can be done through continuous variable valve lift on NA engines.
But our conversation was about driving the car near its peak power output, i.e. full throttle acceleration. That's when torque steer really becomes apparent. You wouldn't feel torque steer at all during normal driving.
The only correct way to determine a car's acceleration is to give the customer the full torque curve and the transmission ratios, as well as the dynamic weight distribution and tire grip. But it's unnecessarily complex. If I need a rough estimate, I only need to know the Power-to-Weight ratio. Do yourself a favor and calculate the power-to-weight ratio values of Lexus/BMW/Mercedes/Audi vehicles and plot them against the 0-60 figures, you will see a good correlation there. But try doing that with the torque-to-weight ratio and nothing will come out of it.