It wouldn't have had the same weight if it was a random Uchiha. At best Izuna was the only other Option since he'd have some connection with Madara. If anything t should still be Obito but executed better. You can keep Rins death in there but show us other reasons and just have Rin be the starting point and by the time of the war make her irrelevant in his mind.
From Rins death we should have seen Obito going from Nation to Nation and learning about the corrupted ninja world, something he mentions but is never shown and is over shadowed by RIN this RIN that RIN is dead boo hoo RIN was my only light.
Maybe go into more detail about his parents and how he didn't know them, maybe instead of being an orphan like Naruto a flash back where Obito kills his parents commenting on how his father always saw him as a failure and this is Obitos rebellion to his father and the clan that rejected him, thus why he attacked the village with the nine tails and why he helped kill the clan, he had a vendetta of his own. This alone would have added layers to Obito.