It’s always present and cannot be hidden by app developers, and so there’s no reason to not populate it, and thus the menubar serves as a consistently available master index of the program’s functions. That alone makes it invaluable.
There’s incentive for the menu bar to be properly populated with all the functions that a program offers. Mac users expect it.
Compare with non-standard Mac apps (mainly Electron apps or ports from other OS), modern Windows apps, and many Linux apps where the menu bar is often a second class citizen or completely absent, leaving you to the whims of the developer rather than enjoying conformance to a system-wide standard.
Mind you, app-defined command palettes can be better than a global one because they can provide more information and context and augment it with other widgets as appropriate. The best command palettes are not just a searchable version of the menu, they add more.
The app-defined palette enables more rich functionality as you’ve mentioned, while the system-owned global menu provides a consistent way to see everything an app is capable of without hunting and pecking through the palette. The menu also serves as a unified API for assistive and automation technology to interact with software and allows users to choose how the menus are displayed (don’t like a top-aligned menubar? Cool, your desktop can present it as window attached menus, a pie menu, or NeXT style floating menus or anything else you can imagine).