There's no technical reason to use less colors in your palette, but there are two non-technical reasons I can think of.

• Working with a more limited palette is a bit easier.
• Picking a limited set of colors ensures some consistency of style.

Honestly, these are both just style choices, in my opinion, so if you want to not limit yourself in terms of colors, I don't think there's anything wrong with just using whatever ones you want and staying away from a limited palette, but that's just me.

Anyway, that portrait is excellent.  If I were to change anything about it, I'd say think about adding some highlights and shadows to the hair, and maybe a highlight on her visor.

Working with a set palette not only ensures consistency, making different sprites look like they belong together rather than clashing like a bad collage, but also sets the mood of the game: bright contrasting colors make for a cartoony feel, or at least a sunny atmosphere; reds, browns, yellows and dark greens immediately say "autumn", and so on. You also want to keep in mind the physics of vision: a level with darker colors, suggesting low light, should also have fewer colors, since our ability to see color is diminished in the dark. (At the logical extreme, remember how Limbo was rendered entirely in black and white? Tell me that's not a striking effect.) For example, your character looks like she's under some sort of pale, diffuse neon light, which fits the cyberpunk theme. You'll want to keep the same effect throughout, if not the same colors. In fact, keeping the theme in mind might help you choose other colors, which in turn will reinforce the theme, starting a virtuous cycle.

So yeah, do think in terms of palettes, even if you don't have technical limitations to deal with. :)

So, your mention of the burn tool actually brings up an interesting line of discussion.  There are a set of "rules" for what makes something pixel art, which can generally be distilled down to "you should know why each and every pixel is the precise color that it is."

Rules like this generally aren't arbitrary (and it's not like there's some Pixel Art Commission out there deciding what is and isn't pixel art), and they often come to be due to the fact that following those rules tends to produce better results or help you avoid issues later on.

That being said, as an artist, your goal is to produce the best possible art for your game in the time that you have.  So if the burn tool works for you and it speeds up your process, then there's nothing wrong with continuing to use it, particularly since your use of it so far hasn't caused any visible issues.  Your art doesn't have to conform to an exact set of processes in order to be good.

Now, there's a big caveat here for other people who might be reading this:  If you're a beginning artist, you should be aware that the rules are there to help you, and to also to help others help you.  If you're new to art in general, it's a good idea to follow the "rules" of whatever art form you're working on, because those rules help you avoid making beginner mistakes.  When you reach KiEN's skill level, you're probably safe breaking the rules, provided you know why you're doing so.  In OP's case, using the burn tool is a shortcut that allows more art to be produced faster with little or no sacrifice in final quality.  In general, if "that's my style" is your reason for breaking a rule, then you probably shouldn't be breaking that rule until you've mastered a "style" that involves following the rules.