Doesn't this require foresight that your mouse may fail? It isn't enabled by default.

Any other OS, you'll be able to at least tab around without the mouse.

What's missing is discoverability -- something Apple used to claim to care about.

To your credit, this does indeed work, but I won't retract my point. It's super-kludgy to go through everything like this, and I definitely can't leave it on all the time. I'm spoiled by the innate tab, shift-tab options of other operating systems. Ironically, when I tried to turn on the accessibility feature just through keyboard nav of Settings, I failed to get to the checkbox (there is at least a global Accessibility shortcut...if it's switched on).

I'm at a loss to explain why this particular navigation issue shows up in the Settings app. Other, less critical parts of the OS actually work fine.