[1] Shifting in this manner is also used with synchronous manual transmissions, particularly after a clutch failure, to prevent destroying the synchromeshes with the power of the engine.
If they back off enough, a moment comes when the engine is neither driving the car nor being driven by the car; at that moment the stick moves freely, and the transmission "effortlessly" shifts out of gear.
To shift down, the driver similarly backs off on the accelerator and "falls out of" the current gear, but then pushes a little harder on the accelerator to increase the RPMs enough to match and allow them to "fall into" the chosen lower gear.
[3] Float shifting can reduce clutch wear because it is used so much less (only for starting from a standstill).
Conversely, improper engagement of a gear (when the engine and transmission speeds aren't matched) can cause wear on the synchros and lockouts, and damage the gears by physically grinding them together due to a difference in speed.