I always thought it had something to do with the mechanics of a loudspeaker, with a positive transient the speaker starts moving out and negative is starts going in. Maybe you gat a bigger ooomph when it starts going out ?
I am not sure whether this is really audible in itself with a single sound.
However, it can make a big difference when layering sounds (e.g. kicks) with different phases, i.e. softening when phases are opposite and emphasizing when in-phase.
It would displace more air if you “wind it up” by pulling it back and then pushing it suddenly forward. However, this would probably only work if that is the only sound to be played and if you are precise with your timings… Other sounds would displace it back and forth as well undoing all the work done to pull it back.
Massive lows are, sadly, only really achieved with big speakers. There’s an equation for the cone diameter in relation to Hz. and you need HUGE cones for, say 20. That’s the importance of labyrinth designs and the like in modern subwoofers, still, if you get top of the line equipment, look at a concert rig: subwoofers are still, by far, the largest single speakers (by a huge margin) in, say, a line array.
A more viable avenue would be psychoacoustic enhancements or killing the difference between quiet and loud parts (with the byproduct of exterminating dynamics i.e. Compression).