Did you read the link I provided in the link to the "Subwoofer Myths" thread? That issue is addressed. As long as the woofer has the motor capable of pushing and pullling the mass to the distances the driver is designed for, there is no issue.
Here it is if you missed it
The trade off for your way of describing it is the output is significantly lowered and thus requires more drivers to achieve a set volume.
Why is it that the JL Audio W7 series woofers are some of the most accurate drivers on the market in terms of motor and suspension linearity, yet boast some of the highest xmax numbers available for their size categories, specifically the smaller drivers????
Your analogy is flawed to a fairly large degree.
That is like saying a small car will be faster than a bigger car because it should be able to accelrate and deccelerate quicker since it is smaller and thinner. That makes no sense. There are too many variables involved that play into the equation with woofers or cars than simply the size of the cones or the cars.
If the bigger car has an appropriate amount of horsepower/torque and braking system it will/can be every bit as quick as the smaller car or faster.
If the bigger car is made of carbon fiber composite, (weighing 400 lbs. less than the small car), a ceramic/carbon brake setup, and 300 more horsepower it can easily match or beat the small car.
This is not the best analogy but more fitting.