It is incredibly dangerous.
Loosely astride a 1000 pound temperamental animal, encouraging it to accelerate in the middle of a pack of other stressed beasts has it's risks and takes more courage than most people imagine.
Every jock gets hurt at some point or another in their career, if not maimed, paralyzed or killed.
It is a hard cruel life.
On the other hand, you will see many women in the less dangerous sport of harness racing. Women seem to have more of a sense of self preservation.
You also see plenty of women in the eventing sports (show jumping, dressage, cross-country), and they often win against men too.
“The jockey is just along for the ride.”
I agree with everything you said. One little stumble and the jockey is most likely going to be on the ground hoping the ambulance is not far behind.