Even though I could agree that DNA holds the chakra of its user (for instance, Sasori's puppets), it doesn't change the fact that from the origin of this manga, the Sage of Six Paths and the Juubi were the sources of his Elder and Younger Sons.
First, we know what is Yin Energy (or Yin power) and Yang Energy (or Yang power):
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Essentially, we can talk about Yin Yang Power to the ability of create a living being, so we can use these variables to compare the abilities of a living being.
Now, the Body and the Eyes were from the Sage (this is the DNA) and the Physical/Spiritual Energy (chakra) came from the Juubi.
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(People used to make the rebuttal that the Sage already had chakra, but this is not true at all. The power the Sage had was inherited by him from the Fruit Kaguya ate before his birth, so great part of his chakra reserves are from the Juubi itself).
So Rinnegan as a live ocular organ is the combination of four variables:
Yang Energy (Lifeforce/Vitality + Physical Energy), Yin Energy (Imagination + Spiritual Energy), Uchiha DNA (The Eyes) and Senju DNA (The Body).
Madara was able to awake the Rinnegan because he met the four requirements:
- Yin Energy (from himself)
- The Eyes (his DNA)
- The Body (Hashirama's DNA)
- Yang Energy (it was not from the dead cells of Hashirama... this was given thanks to the Yang Energy provided by the Gedou Mazou's chakra, that gave in essence, Lifeforce, because he was being nurtured by chakra with Yang afinity. That's the reason Madara could survive for so long).
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By the way, it's not like the reason Madara survived was chakra... Sasori's puppets are death but they hold chakra, so chakra alone don't give life to things. It is Yang chakra what gives life!
There is when lifeforce comes at hand... Mazou's chakra is full of lifeforce, and henceforth, we got the reason of why Madara could last so long:
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And to put the cherry to my rebuttal... Hashirama barely got chakra in his current state:
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since Madara stole the rest.
Summing it up: Sasuke lacks Senju DNA, an essential requirement for the Rinnegan.