Do I need to zero out a new disk after formatting it?
Zeroing out a brand new disk is, for the average user, a waste of your time. Writing all those zeros to every single block on the disk is time consuming (and yes, your zero-out time seems to be in the ball park even for USB 3) and has no real benefit. The disk, if new, and freshly HFS+ formatted is ready to go without any additional work.

Zeroing out can help the security-paranoid erase latent data from the platters (though, zeroing isn't sufficient to meet US Government regulations for sanitizing media see NIST Special Publication 800-88 for more details). And it can help find and mark bad sectors before you start relying on the media for day to day use. I'll contend that, except for ultra rare cases where new media is heavily damaged on arrival, that modern methods for finding and marking bad sectors in situ are good enough to make pre-finding them before serious use unnecessary in this day and age.