Tbh, the rinnegan—sharingan relationship becomes convoluted by the late war arc / Juubi resurrection arc. I don’t think Kishi intended for it to have as many unique abilities as he eventually gave it, it was a byproduct of escalating stakes.
For some cobbled together lore answer? He wasn’t taught them. Obito taught Nagato most of his rinnegan jutsu, so he probably left out the truly dangerous ones.