Damn! not these sage being an uzumaki threads again! i like your thread btw,but it has been stated by obito that nagato is of SENJU lineage.so that means uzumaki is connected to the SENJU,which could be comprehended as that UZUMAKI and SENJU are clans deriving from the younger son because of their strong bodies and life force just like uchiha and probably hyuuga clans are deriving from the elder son because of eyes and spiritual power.
madara would have given the rinnegan to obito if he had met him first,but he gave it to nagato first....so why would obito bother stealing nagato`s eyes(which would be f%(/&)cking hard to do considering nagato is a strong dude)when he could win nagato to his cause,let him develop his already developed powers,use him,and take his eyes when he died?? i think this is a way smarter choice because there is no way obito could take nagato`s eyes at that time.
but you`re probably right on the account that nagato had a better body to develop and use rinnegan`s powers on a greater scale because afterall obito just had some portions of SENJU DNA,while nagato had entire body and stamina of the younger son because of being an uzumaki