On the pics, one by one:
1. Good example. A few high-saturation colors on a screen wherein the vast majority of colors are low-saturation.
2. Again, the vast majorty of the colors in this picture are low-saturation.
3. A good reason why
not to go high-saturation. The screen is too visually busy; it's difficult to distingish between background and foreground,between important and unimportant. Where such a distinguishment cannot be made by the three-dimensional process of focusing in the eye, it must be made visually by other means.
4. Again, low saturation. The life hearts are the brightest thing in that picture.
5. Is that a photo of the screen? Things in Star Fox don't generally glow like that.
6. Your first example of a high-saturation picture that works. In this case, it's due to the high degree in contrast between the exceptionally busy (but unimportant) background and the very clean play area. Again, visual contrast is the key.
7. I just have to ask, do you honestly think that looks
good? 90% of the screen is one shade of one color. This example is also, in my opinion, irrelevant; they only had a few colors to work with due to technological restrictions, and so had to choose a broad color palette for flexibility. We have no such restriction, as evidenced by the fact that I use more colors in my character sprites than were used in that entire game.
You can't just say "hey, the games I played on the SNES had bright colors, so all our colors should be bright and saturated!" You'll come out with a visual mess, especially if we include a high degree of detail (as we really must, to create an interesting overall world).
You also have to take into account location, style, and feel. I, personally, don't like how highly saturated the new woodland tileset sprites are, because it doesn't give the sense of being woodland; woodland implies a lot of tree cover, which means a lot of shade. They tend to be dark. These are the same sort of considerations that were made in the games you're looking at and all similar games, except in certain specific cases wherein considerations like that were deliberately ignored. If you want an easy example from a game I'm rather sure you'll take into account, let's compare the grass tiles that have been largely the center of this debate...

...with the grass tiles from SoM.
Edit: fixed image link
See what I mean here?