Yeah why do pixel artists advocate tinier palettes?

For myself I think rather in terms of lengths of ramps than in overall color amount.

the "nostalgic" side:
super simplified shading approaches (and not 100% realistic, but let me generalize):
NES uses 3 colors per ramp
SNES uses 4 color ramps
NEO GEO uses 8 colors per ramp

A NES game is simpler than a SNES game and this is simpler than a NEO GEO game. Of course there are some NES games which are more elaborate than SNES games and SNES games which are more elaborate than some NEO GEO games, but for a general approach you could say:
you need to hit those general color limits/restrictions to evoke a real "retro" feeling that your game is rooted in a certain technical period - e.g. Shovel Knight did this to a good extend.

the "project-developers" side
The more colors you use the more work it is to put them down.Shading will take longer wth more colors
If you compare Anime OVAs and anime TV shows the OVA's are usually higher quality. Sometimes those animes use more shading.
More shading takes more time and therefore is more expensive - of course it can look better (not necessarily though, if done wrong)
On a project scale it can make a difference of thousands of hours to use more elaborate or less elaborate shading on elements.

the "artistic side"
Art is a super complex thing and problem solving on equally high levels as elabrate mathematics once you start seeing the more scientific side of things.
If I tell beginners to use less colors, it is because the most basic contrast works with 2.
If you fuck up the shading with 2 colors, you also will fuck it up with more.
If you fuck up the contrast with 2 or 3 colors, you will also fuck it up with more.
If you try to learn a skill you try to eliminate all the noise and just practice the thing you suck at in order to get better at this very specific thing.
Many beginners struggle with very basic things like big proportions, contrasts, basic color choice ... etc.
Working simpler costs them less time to play around, iteration is faste rpossible and the psychological attachment you have to something you haven't spent dozens of hours on is less, which is good for experimentation.


the "game-designers" side.
The more colors you use in little spaces the more stuff blurs.
Blurring is pretty bad for all types of art and hinders quick recognition, which especially is bad for games.
For games you want to have a clear image right away to present the player the challenge in the quickest way possible.
For quick action based games, an elaborate blurred artstyle could get in the way of readability and cost some additional milliseconds.
THis might sound not much, but if you ever watched high skill fighting game fights, LoL matches or any other E-sport you will see that this could become a super valid problem. And it is for some games.

And another thing you might consider:
Pixel art is placement of pixels.
if you work in a 4x1 canvas you can't use 5  colors.
if you work on 16x16 it maybe isn't really worth using more than 4 colors per ramp considering that you have shapes to shade and one color might go to waste.
on 32x32 you easily could get away with 6 colors or more and it might even look much better.


So there you have my views on the topic.

the elllipse should be 4:3 in ratio

Here you have the calculations / tut
http://cyangmou.deviantart.com/art/Pixel-Art-Tutorial-4-3-4-cylinders-and-cuboids-329318036

check out "Tower 57" which i illustrated, I am fairly sure that all objects in it are angled the right way:






Zelda breaks projections in multiple ways for gameplay
stuff like Earthbound and similar games uses 45° top down, but in many cases not a realistic approach to shape and volume.
Which means characters are drawn nearly from the front, while some things appaear seen from the top, it's not consistent but it usually works if the angle difference is not too strong.
THat being said the more realistic the style, th emore those things matter.

seems to be pretty great, considering how minimalistic it is.
YOu maybe want to use a brighter color for the plume than for the shirt, to make it pop in the north frame

Game: Beyond Oasis
Release Year: 1994
Platform: Mega Drive

This  is the oldest game I know of which falls pretty much in line with the modern "cluster approach" of pixel art, and despite some dithering here and there the whole thing is scaringly similar to a lot of techniques displayed in current pixel works.

Interestingly enough this game already used quite a high resolution for their assets and generally feels really clean and colorful and while this prodction is kind of pioneering many things so commonly seen today, and there are already so many great choices evident, that it's just worth to take a look.

I made a collection with various backgrounds: