Here is what I think about Nagato and his Rinnegan.
First of all, it seems unlikely that Madara was able to give Nagato his own Rinnegan as transplants. From what we saw in this week's chapter, Madara was extremely old when he saved Obito from his death. Nagato is much older than Obito, which would not make sense if he 'awakened' them when he was a child.
My thoughts on this particular subject is that Nagato was shown to be a master at the Rinnegan. If we compare him to Kakashi for example, the mastery of Kakashi's transplanted Sharingan versus the mastery of Nagato's Rinnegan are on different levels. Kakashi is not able to access the many available techniques that Sharingan provides, yet Nagato has the ability to access every Rinne technique. Also when someone like Obito transplanted a Rinnegan into his eye, he was not able to have the complete mastery of the Doujutsu either. These two examples are not on par with the strength of ocular prowess that Nagato has shown with the Rinnegan.
Maybe instead of directly giving him the eyes, Madara could have given him some of his DNA instead. The combination of Uchiha and Uzumaki(Senju) DNA would allow him to 'awaken' the Rinnegan through his natural ability, thus eliminating the fact that Madara would have to give him his own eyes.
Either way, Rinnegan directly given to Nagato or not, Madara has a collection of Sharingan available to replace his eyes if needed.