I was more arguing from "real life", to be honest - but good point there.
On range... I'd argue that the extra range of bows is very unlikely to be used by Ling Qi. For one thing, if an opponent isn't within her mist, a lot of her other capabilities are inapplicable or weakened - so she's going to want to be closing to throwing knife range (that's 25 meters for her) *anyway*. And with Sable Crescent Step, she's quite capable of doing so. Really, most combat will either occur within the range of her knives or she'll be both motivated and capable to closing to under that range. Plus, the knives can be used in melee - a bow... cannot (and, again, switching between bow and flute is a lot harder).
EDIT: Plus, the bow is a primary weapon, often used early - because enemies will almost certainly close the distance against a bow themselves. Early in a fight, Ling Qi is going to want to set up her mist. If she delays doing so to shoot arrows, then she's not going to have a lot of time to do so when the enemy closes in. If she puts up the mist first, then enemies are probably well within knife throwing range anyway.
Really, a bow is only useful when:
* Ling Qi is ambushing from range.
* She's in an archery duel... probably with someone who specializes in the bow, while Ling Qi herself only dabbles. In which case, why on earth isn't she closing the distance and clouding their vision with mist?