Why would that happen if fusion became viable? It didn't happen, and fission is already perfectly viable.
Think about it.
Nuke plants are horrifically expensive to build, have significant drawbacks regarding waste disposal, and require insane amounts of monitoring and maintenance.
And, at the time, an all-electrical society of the kind that is now being pushed simply wasn't viable. Electric cars weren't viable, coal, oil and gas as fuels were significantly less expensive, the list goes on and on.
Now, however, fusion has the potential to supply virtually unlimited amounts of energy with virtually none of the waste that nuke plants generate and fission systems have potentially unlimited lifespans with very little of the kind of maintenance that dooms nuclear to being as expensive as it is. Electric vehicles are far more viable now than they were at the start of the nuclear age and coal, gas, and oil are becoming progressively more expensive.
Edison, Tesla, and Westinghouse all saw the potential for a world powered by electric with virtually no need for coal, gas, or oil. If fusion actually becomes a viable energy source, what they saw becomes a distinct possibility.
Yes, there would still be need for oil to some degree for lubricants, industrial uses such as plastics and the like, but with the power potential offered by fusion the price of oil would, over time, plummet and become largely irrelevant.
