Most characters that use WDing apply it as a form of burst movement. So for Falco (not Falcon), WDing is faster than his dash, but it takes a bit longer to start moving. If I'm trying to dodge an attack, being stuck in jumpsquat for 5 frames and then taking a few more to actually start moving away is too sluggish. If there's no imminent threat, however, those startup frames not only become irrelevant because my overall movement is faster, but it can make you more deceptive because the opponent can't react to your jumpsquat and interpret it as movement, whereas if you see a character dash, they lean forward and it gives a much earlier visual cue.
For Falcon, his WD is not so great (ranked 17th from the whole cast) and his dash and run speeds are
by far the best in the game by any sensible metric. This ends up meaning he doesn't have a whole lot of usage for his WD in neutral. His dash not only has superior speed, but it goes so long that WDing before dashing back, to avoid an approach for example, isn't really necessary.
The one main instance where WDing would be useful after an aerial is if you shield because you expect an attack. One huge advantage to WDing over dashing is you can WD out of shield. Falcon mains typically try to avoid shielding, and his dash is so good he can usually just dash away to be safe after aerials, but when you do feel forced to shield, being comfortable and fast with WDing OoS as soon as it's safe is good to know.
With all this "on paper" analysis, if you still feel like experimenting and want some inspiration, Hax's Falcon was notorious for his heavy use of WDing. Obviously, there isn't much recent stuff, but he has played in a few Falcon round robins that you can look through.
Source for the movement speed information.
