Not only is it not necessary to hand-write the address if you have a label, it may be confusing (at least for a human handling it, I don't know about the automated machines).
Those labels are meant to speed up the processing, and writing all over next to the label may just defeat the purpose. This is especially true of tracked services (Tracked Packet, Expedited, Xpresspost), where the bar code may be read automatically.
I've never, ever, had a labelled item go astray in several years of selling (mainly to the U.S. and overseas). I think I'd say that's pretty reliable. 