sometimes people get too accustomed to ASC (LOL really) and I'd throw in a HA in. Also, since past a certain point, people forget you have it, it's sometimes lulzy to double jump and then use HA to "stall" right before you hit the ground, at which point a person might miss their grab.
As for its uses offline against competent players, I don't really know LOL.
I do use it sometimes to wait for an opening if someone's ledge camping - go slightly under the level and let HA rise into the bottom side as it's rising. On BF, if you do this, you can bounce yourself towards the center crystal, wall jump, then spring back. On FD you can do that against the wall under the lip ledge thing.
I guess for offensive uses, it's probably better off as a followup after an spindash hit (any phase, lol). Forever ago, Terios had an offstage D-air > HA pseudo-combo but everyone's too scared to try it LOL