...was because he wanted to revive Izuna, because Madara and Hashirama would both have one brother.
That's not actually a terrible theory. At the very least, we can see several possible reasons here why Tobirama would develop that Jutsu. Maybe Tobirama intended to use it on himself to allow himself to die for peace. Or he intended to use it on Hashirama, because Hashirama would commit suicide before he ever allowed Tobirama to die.
Maybe it actually was for Izuna.
But then again, Madara had his EMS, and would have been able to learn many new secrets from the tablet in the Naka shrine. Maybe he would even have learned the secret about unlocking the Rinnegan, and knew that if he did that he would be able to use Rinne Tensei to revive Izuna himself.
It's very interesting to think about, because Madara says he won't trust Hashirama until one of the Senju brothers dies. But we know from history that he DOES eventually form an alliance with them even though both of the Senju brothers are still alive at the time. I wonder what changes his mind? Is it because he knows about the rinnegan?