The Infinite Tsukuyomi was not all about Rin. Rin dying was the main trigger for him to change sides, but not the only reason.
He says that while he travelled under the identity of Madara through the world, he saw how bad things were and that's why he decided to move even more forward with the Tsukuyomi plan.
Obito meant to help the world itself, even if it sounds ironic or even dumb.
As he says, Rin is someone who isn't meant to die, what caused her to die at that young age, alongside many children sent to war, was the current state of the shinobi world, just like he says
The shinobi system... the village... what's created all these circumstances...
Therefore, he realized things had to change and he went forward with the Tsukuyomi plan.