Why doesn’t Keynote support \pdv command?

You must follow the guidelines set by the blahtex translator incorporated into Pages, Numbers, and Keynote regarding accepted La[TeX] syntax. Apple has not installed any form of TeX distribution or \usepackage capability in its La[TeX] to MathML translator. You can find the blahtex PDF manual in:

About LaTeX and MathML support in Pages, Numbers and Keynote - Apple Support (IN)

The following was done in Keynote v14.4 on Sequoia v15.5:

Apparently, all those fancy shortcuts like \pdv come from various "packages" that people download from the internet and install.

Apple doesn't support that kind of "mix-n-match" practice for any of its apps. You have to learn the actual LaTex syntax for these things instead of using packages.

I know nothing at all about LaTex and it was trivially easy to figure it out:

{\Delta}f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial ^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}

Really the hardest part was finding an example where someone asked this identical question (as they have for decades) and, for whatever reason, this one time, someone didn't respond by recommending one of a dozen different packages, each with a different syntax.

This is not the place for feature requests. It's just a user-to-user forum.

To provide feedback (including bug reports and feature requests), use: Feedback - Keynote - Apple