I believe it's actually the other way around. The primary applies to the mount and the secondary to the man. If the mount collapses, the guy dies too.

It's the same way with elephants. The unarmored aspect of the riders make for those funny moments when the individual riders on the eles get picked off by your archers.

They should definitely allow you to target the riders separately. Anyone played Homeworld series before? One coudl target separate facilities on capital ships. One should be able to target riders on eles and with all riders killed, the ele should go amok without even the chisel option.