Anivia's passive is coded as a champion. Nunu can't consume her for the same reason he can't consume other characters. Syndra can't throw her for the same reason she can't throw other characters. The only reason that you can use those abilities on Zac passive is that it's coded as a minion.
There are benefits to both. Anivia passive can TP to safety as long as she starts the channel before being egged and can also take Thresh lanterns. Zac passive can have an ally TP on it so that he is guaranteed a respawn. Also Anivia's egg has reduced armor and MR before level 12 (starting at -40 from base to -10) before finally being equal or better to her stats while alive.