AFAIK, BR and CI's midnight departures from LAX/SFO to TPE, as well as CX's LAX/SFO-HKG, are more popular than the afternoon ones. Fares for the late flights are also higher in general. Part of the reason is the onward connections they offer, but a good portion of local traffic also prefers the early am arrival. YMMV, but I do feel that I've lost a day when I arrive in Asia after a 12-hour trip, only to encounter bedtime shortly thereafter.
With the 788/9 in full deployment, I can envision late pm/early am departures to ICN and PEK complementing the afternoon flights. That would make a somewhat impressive mini-bank with flights to HND, SYD, and SIN.