I'm gonna doubt you when on they own website navigating is really bad.
Only tab and shift-tab. Arrow keys are a bust. And the only visible shortcut is ctrl-K for the search input and I think it's because it comes as an algolia default.
For something better I only have to watch around the page at the browser itself: underlined letters in the menu tells me what alt+letter will open said menu. Then I can navigate using arrow keys and most menu items are shown with a key combination shortcut.
If I could show you some of the apps I've built with it would probably change your mind. A few had to go through testing and validation for accessibility. That and I'm pretty firm on keyboard navigation for all things. Had to tweak the corporate colors a little bit to fit WCAG compliance on the contrasts.
One thing that was crazy was having to go through verification for blind usability, when the core function (validating scanned documents) requires a well sighted user.
I won't say MUI is perfect... it isn't... but you can definitely go a lot farther in a browser than you can with what's in the box with most ui component libraries is the only real point.
I'd like to see those accessible frontends. The majority is not usable keyboard-only.