What If Saruman Doesn't Join Sauron? *spoilers*

A main point of the story is things happening the way they were meant to happen. Even evil which is worked out for good. Bilbo was meant to find the ring, and Frodo was meant to have it - as Gandalph explains. Providence is an important part of the story.

Saruman only pretended allegiance to Sauron. He believed that if he could obtain the Ring for himself that he could manipulate its power to his own will and in the end he would be the Lord of Middle-Earth. He was wrong. What you present looks interesting but that requires a more robust reconfiguration of his character, not just a readjustment of his situation.

Back to your alternative summary: If Saruman had no interest in the Ring it would have meant an entirely different lot in life in Middle-Earth. He probably wouldn't have spent time holed up in Isengard and his interactions with the Free peoples probably would have helped strengthen not only Rohan and Gondor but the mostly inward looking Elven realms of Mirkwood, Lorien, and Rivendell. Also, since he was a subject of the Vala Aule he could also have had more interaction and provided assistance to the Dwarf Kingdoms who had their own conflicts with goblins and orcs raiding their treasure. Utlimately though, the lure of the Ring's corrupt power would eventually destroy someone in the fellowship. You also have to consider that people like Denethor were already being corrupted by Sauron via his own use of a Palantir (not s,hown in the movies) and Sauron being as cunning as he is would have used people against each other so even though with Saruman out of the picture another scenario where power and fortune is desired by a lesser group of people not counted amongst the free peoples could have found allegiance to Sauron. If you read Akallebeth in the Silmarillion you see just how cunning Sauron was with even the most powerful of the higher kingdoms.