Totally agree - the landings are [usually] a bit softer too if it all goes horribly wrong. Trying to ride as slowly as possible on grass is another good handling skill/confidence builder. You will fall over, but you learn about where to put your weight - and not to stick your hands out - in a virtually painless way.
When I was teaching horse riding, I used to always tell the kids that you need to look where you want to go. If you look at the ground that's where you'll end up. I have a fatal attraction to potholes and damaged road edges, can't stop looking at them, so that's where I end up. The head is pretty heavy, and so massively affects your balance. I bet you can't take your eyes off patches of gravel now, can you TWA? And just like horses, bikes sense your fear. When you tense up your back and shoulders you instantly become less able to deal with lumps, bumps and changes of direction. I have to really tell myself to relax my arms and shoulders on fast descents - then they act as shock absorbers rather than....er, can't think of an analogy, but you know what I mean.