It's because Nintendo put shit on lockdown in between Famicom and NES.
Third parties were allowed to manufacture their own carts in Japan, because the whole third party thing there evolved by accident and Nintendo wasn't necessarily thinking about that when they designed the console. Both official Nintendo partners and unlicensed ones made their own carts (there was no copy protection chip), so that's why there is such variety in cart styles.
When they came to America, they changed the whole deal. Nintendo made all carts themselves. Third parties were forbidden to make their own. And they put the 10NES copy protection chip in the console so that no one else could make them without great difficulty. They slowed pirates, and made all the third parties dance to their tune in order to secure a share of the limited carts. Every single NES game you see probably came from one or two factories in Japan, and that was true for every Nintendo console after that point (+Mexico), until the Wii.
Sure, Nintendo could have made their own carts in different colors (they did in Japan).. But I think because they were manufacturing millions upon millions of them for themselves and countless third parties, it made sense for them to just be one standard style. It would have to be a very special case to make a tiny percentage of them different.... And of course Zelda was that special case.
Plus I do think there is something to the fact that they wanted to make it look less like a kids toy, as you said, and redesign it from a kids game console (which were dead in America) and more of a family "entertainment system". Plus in general Japan seems more forgiving of multiple colors in logos and such (you see it a lot there), while Americans, maybe to this day, view that as being childish.