It depends on the context.
Take for example the dance to SNSD's ITNW. It's pretty badass, especially, the ending breakdown.
Could they ever perform this choreography without lip-syncing? Not a chance. Their live performances of ITNW today also have watered-down choreography. And if SNSD never lip-synced a day in their life, then I never would have gotten to see the above, EVER.
natme said "If those girls can't sing the lyrics and do the choreography at the same time, then it either shouldn't have designed to be outside the limits of the performers or they shouldn't be on stage," and artists like BoA have the chops to be able to sing and dance at the same time, but to watch BoA let loose completely on a dance without having to hold back due to singing constraints is something special.
There's also logistics to consider. Wireless headsets just do not capture sound well, and even wireless hand mics can suffer problems when trying to stage a huge arena-or-larger concert in which performers are football fields apart. There have been concert performances where I felt underwhelmed because all of the static coming through the mic was too distracting. AKB48's Lay Down is a favorite of mine because of how the girls get to slouch around sexily, but the way they're grouped around the mics would sound absolutely awful live, with people fading in and out depending on their proximity to the mics. Trying to mix that would be a nightmare, and the only way to fix that would be to change Lay Down's staging to something way more boring. No thanks. As BarrieV pointed out, atmosphere is very important. Consider the following performance:
Lip-synced. But damn, Ai is just dancing so dynamically, and the fact that she hit those notes even in studio is amazing, (plus, because it's a shuffle, that recording isn't available on a CD) and the arrangement by itself is so frantic that it gets my blood thrumming. Sometimes it's more important to preserve the spirit of the song, even if lip-syncing is required. Queen never performed the "mamma mia" portion of Bohemian Rhapsody live because it simply could not be recreated live: the original portion involved each singer dubbing over their own lines 20 or so times. Similarly, Perfume get vocoded for their songs, even live, because it just wouldn't be the same with natural vocals.
That said, if a performance's highlight is mainly in the singing, then of course it should be performed without lip-sync. I'm thinking of things like the adlibs in Taeyeon's Hush Hush, IU's Good Day, and BEG's Sixth Sense. On the AKB48 side, songs like MARIA and Bird. If the girls can handle singing and dancing easier choreographies live, then by all means have them do so.