Think of it in a simpler way: Maximum acceleration happens when you produce the most horsepower from the engine and send it to the wheels. As long as you're near the HP peak, you're getting maximum acceleration.
Yes, you're right that in any particular gear, you acceleration will be greater with lower gearing, but I'll still be in 1st after you've had to shift to 2nd, so at that time my overall gearing is lower, so I'll accelerate more than you. Then I shift and we're both in 2nd and you're gaining ground, then you shift to 3rd, I'm still in 2nd, I gain ground, etc..
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