Did you ever notice that every item, human, and non-boss enemy in Zelda is made of one of exactly four palettes, each of which is made of only three colors (plus transparent)?
1. Link's tunic color, his skin tone, and his hair color
2. White, orange, red
3. White, light blue, dark blue
4. Black, dark teal, and red
For example, #1 is used for Link, Zelda, the merchants, and the raft, which is why when you get the blue ring or the red ring and your tunic color changes, it also changes the color of the other people's clothes and the binding on the raft.
Here's a graphic I made of every sprite in the ROM six times -- one with the three versions of palette #1 (no ring, blue ring, red ring) and one for each of the three other palettes: http://i.imgur.com/omBWovb.png
It allows you to see that, e.g., Wizzrobes are made of only three colors, and they're the exact same three colors as the red candle, heart containers, tektites, like-likes, octoroks, rupees, the boomerang, the map, fire, the life potion, fairies, and the master sword.
It seems this limitation/concept is something that I haven't seen too much in modern pixel-art. We often see modern pixel art using larger pallets, but just low resolutions.
This is the problem I have with the widespread use of pixel art. Most of it is ignorant of why the old graphics looked the way they did. Like you said it is adopting one of the limitations but ignoring the others.
The developers of Shovel Knight actually emulated the way NES graphics work (and added some enhancements to it) and the result is a much more convincing retro feel.
Here's a graphic I made of every sprite in the ROM six times -- one with the three versions of palette #1 (no ring, blue ring, red ring) and one for each of the three other palettes: http://i.imgur.com/omBWovb.png
It allows you to see that, e.g., Wizzrobes are made of only three colors, and they're the exact same three colors as the red candle, heart containers, tektites, like-likes, octoroks, rupees, the boomerang, the map, fire, the life potion, fairies, and the master sword.