This felt like a Uzumaki wank theory.
But uh, going with the cannon one. Madara did not have a Uzumaki DNA, pure Senju dna and Uchiha Dna. Just like the Rikudou.
Nagato can't be the 2nd Sage because he was GIVEN the rinnegan, Madara in aspect of the Rinnegan is the second Rikudou.
Nagato was given the Rinnegan because of the following reasons:
- Boy in war
-Uzumaki, hence contains Senju dna
- Someone who experiences war will be easier to manipulate
Basically Nagato was more beneficial.
And Senju have higher Chakra reserves..

. Even the so called "Uzumaki +Senju" hybrid Tsunade is recognized as a full blood Senju. Why? Because there is no difference between the bloods, except Senju are physically stronger.