Not Palatino.
And most of those fonts have licenses that are inconvenient at best. The only thing that allows them to be packaged for Linux distributions is Microsoft's '90s-era "Core Fonts for the Web" initiative. This initiative is long discontinued, and so the fonts cannot be downloaded from Microsoft anymore. Only the '90s versions of the fonts are free. Worse yet, the license forbids packaging the fonts in any way other than with their original 32-bit Windows installer, which means that hacks like cabextract are necessary to install them on any other system.
Instead we're restricted to only a few fonts that actually have decent cross platform support.
It’s kind of the same problem as saying that the browser should include common images. Which images? Why? How many?
Images follow a different usage distribution than fonts. I'd say that the top 100 fonts are enough to render most web content, for images I'd say this is obviously different, the top 100 images might appear often but not as often as the top 100 fonts.
Google is already distributing the equivalent for text, in the form of the brotli corpus which ships in every Chrome installation.
Well, pontificating here:
1. Because many applications don't ship with additional fonts, and it's an additional layer of complexity. Some do—Microsoft Word comes to mind, IIRC.
2. Because you're still left with the same problem: unless all browsers can agree on an additional set of standard fonts, you as a web developer will only want to use those installed by Chrome and Edge and Safari and Firefox.
3. Because licensing for desktop application may (?) be more of a pain than licensing for web usage. Which may not matter for Google Fonts, since they may be the license holder for all anyway. I don't know.
The challenge is that to ensure consistency, you need to use the "lowest common denominator" of fonts that are installed by default across all operating systems. Which leaves you with (like) Arial, Times, Courier, Verdana, Georgia, Palatino, and (hahahaha) Comic Sans.
The real answer here is why web designers use Google Fonts as opposed to embedding their own fonts. To which the answer is: it's so much easier. (Tech, licensing, formats, compatibility, etc.)