Every image I've seen of NZ football teams up to 1981 has them in Black tops and white shorts.
I love how you insist that white isn't one of the national colours, then post a picture with NZ playing in both black and white

Anyways, at the library now, and the first ever NZ team (1904) wore white tops, black shots and black socks. Same in 1905.
1927-1967 was black tops, white shorts, black socks (same as your post), though NZ wore white/black/black at home in 1948 (this may have been an allowance for the dark-shirted Australian team. I don't know whether or not "home team gets first dibs on kit" was in effect then). 1947 was all black. 1965-66 has a photo at the Basin with white shorts, white socks, and black/white stripes (a la Newcastle's top) against England.
Nothing on the 70's, and everything after 1981 is obvious.
So while black was dominant for at least a forty year period (I can't speak for the 10's or 70's), white was the original. That reason alone doesn't make it more important than the black kit (ie Wellington rep rugby started off in red and blue, yet I see no reason to change from black and gold), but that + 1982 (and for that matter, the amazing efforts of our girls last year - NZ football isn't just the senior mens team).
Both colours have significant places in NZ footballing history - black in quantity, white in quality. Considering all of NZ's signicant success has been in white, and is currently white, and is associated in the general community as white, I'd stick with the status quo but insist our away kits stay black.
TBH I wouldn't mind compromising - reverting to the original & pre-"All Whites" white kit with black shorts and socks, with out alternate being black shirts, white shorts and white/black socks. That way the name All Whites can stay (even if only in an unofficial, White Noise endorsed capacity), more black can be included instead of just as trim, and we avoid having alternate kit colours that aren't official (such as recent blue, or previous reds and greens).
Also, 100% black looks terrible

The best All Blacks uniforms were the ones with white collars.