[Nikkolas]

Fact: No one could willingly throw the One Ring in Mt. Doom.

it was sheer dumb lack/the Will of Eru/Plot Contrivance that allowed Frodo to complete his task.

Other than that, the armies of Sauron utterly eclipsed the remaining Men, Dwarves and Elves of Middle-earth. So the Istari's task, to "guide" the Free Peoples in opposing Sauron, was indeed hopeless because absolutely none of them could hope to prevail against him by force of arms.

So, destroying the Ring was logically impossible, challenging Sauron with armies was impossible....

If you are a general and it is your duty to defeat the enemy, do you put all your hope in chance? Would you trust or follow a guy who's strategy is "well, we can't really do anything but pray they succeed"?

I wouldn't and I don't think Saruman would either. He'd much rather put his hopes in something a bit more substantial.