The 'need' rather than 'desire' argument was for the sake of comparing it to DBZ. Madara did create a need for it, but it wasn't a need to surpass Hashirama. It was not a case of him feeling frustrated about being beneath Hashirama, it was a feeling of frustration and hopelessness caused by living to such an old age and NOT achieving his goals.As plausible as that sounds, I am inclined to disagree.
It was Vegeta's frustration and anger, as you point out, that triggered his dormant SSJ powers. It can also be said it was his feelings of hatred and jealousy. But is it for this very reason I disagree. Why would Kishi make direct reference to this? It seems very unlikely to me that Kishi would use this concept because it fringes DBZ. Plagiarizing this very idea from Toriyama would make Kishi look very bad since everyone knows DBZ is one of his sources of inspiration.
Also, Madara tells us he fought that fight to gain access to Hashirama's abilities and to grab a tissue sample. We also know he lived far longer than Hashirama (since his edo form is so youthful). This is also revealed to us as edo Madara asserts the landscape would be reshaped if Hashirama were still alive to fight him. This means edo Madara is aware Hashirama is long gone. He has probably known this since his seclusion in that cave before he was ever edo'd back to life seeing as he lived until a very old age.
With his arch rival gone, who would be left to oppose Madara? who would be strong enough to make Madara feel so uneasy that he be jealous of their power? Madara may still have a deep rooted grudge against shinobi in general, but he wouldn't feel the same kind of powerlessness and anger that Vegeta felt towards Goku.
So given my above 2 arguments, I don't really think the Rinnegan was unlocked by the sheer NEED for power, since that need was mostly influenced by Hashirama.
So put simply, it was a need created by long-term frustration and despair that culminated in a single moment in time. In addition, this moment was caused by a strong feeling of hopelessness that spawned from the realization that he was not going to be able to achieve the power that he desired his whole adult life.
Again, I don't think in any way, shape or form that the 'need' we are both talking about was a result of his frustration toward Hashirama, but rather a general frustration of failing to achieve the power before he died, which in result caused him to unlock it.