I personally can't get Falcon's throws to combo into anything. Bthrow is fine if you wanna pretend to be Sheik [sort of], but that doesn't strike me as interesting or interactive. Fthrow is for positioning and can kill or combo on bad DI/high percents, uthrow is trash [the move literally doesn't combo vs some people, like Luigi, he just nairs you for trying], and unless there's a dash cancel on dthrow I'm missing, it doesn't combo into knee currently, and it probably doesn't combo into uair or nair [VERY tight timing if it does], while Falcon Kick and Raptor Boost are too slow as well [can tech-chase with them sort of]. If someone wants to show me Falcon's throws comboing even on good DI [down and away], by all means, but the only throw combo I can get is fthrow -> something on really premature survival DI.
But Falcon's throws are useful positionally, not for comboing, at least against people I've seen [again, I might experiment more with bthrow tech chase, which is really silly on a variety of levels anyway... although IDK what his advantage on bthrow is so that might not work]. Dthrow worked ok in the old gravity but the new gravity just messed it up and it doesn't function to do much anymore.
Falcon's rapid jab is useful on shield as opposed to the gentleman because it's nigh-lagless (or seems that way on Wi-Fi lol) and very difficult to shieldgrab - I'll often do rapid jab on shield -> jab1 again to stuff OoS options. Gentleman on shield is definitely punishable, and having rapid jab skip gentleman can help that, but it doesn't need to be AAZ.