Why are the feet so important?

Because if you fall on dirt, there is a big risk you will mess up your feet or ankles without proper boots that protect them.

Well, I rode on the road but can imagine the same goes for off-road, but the right pair of boots makes a huge difference in one’s confidence and ability to securely put one’s foot down at a stop, especially if it’s a bit slick from oil, or loose debris. That, and you can imagine an object hitting your foot while flying down the highway at 80mph feels very different when you’re wearing riding boots vs. wearing vans. Then there’s the whole, sliding on assault aspect.

Well, perhaps not more important than other body parts, but more likely to be injured.

Every basic motorcycle safety class will urge you to get good boots. I just wished I had heeded that advise in time instead of buying them after my first crash ;-/