The higher the Qtc, the larger the resonant peak will be and the less the air in the box, as an envelope, will control the motion of the cone. The cone's mass is subject to the force from the voice coil and magnet making it accelerate and decelerate but it also can't stop or start truly instantaneously because of the mass (inertia/momentum). Heavy things accelerate more slowly than light ones, so the voice coil and magnet assembly are designed accordingly. Air compresses, but the cone's movement has less of an effect on a large volume than on a small one (it's not compressing as much, in terms of percentage), so the air in a large box won't do as much to keep the cone from continuing to move. Everything resonates well at certain frequencies and really well at one particular frequency. For a speaker, this is the Fs. Think of bad damping as a drum with only one head. Tap it, and it keeps vibrating until it naturally diminishes but if you put a head at the other end of the cylinder, it doesn't "ring" as long.
Some music works better with a high Qtc, like Rap and Hip-Hop. Car stereos that were designed for this are sometimes called "one note wonder", because it only does one frequency really well. For the most even response and smaller peaks, more damping is better. A Qtc of .707 is good for a wide range of music and vented systems used for Rap are often in the 1.0- 1.2 range. That would sound terrible for almost all other music. Transmission line and sealed box systems are generally much more neutral sounding.
