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@Oswald
Stiffness is proportional to diameter³ × wall thickness so an oversize bar is stronger then a conventional bar if they are both made of the same wall thickness. However, it would also be heavier. In reality unless the bar is designed for a specific purpose (track sprinter?) there will be a balance of strength and weight by the manufacturer so the two bars will have different wall thickness .. stiffness/mass ratio is proportional to diameter² so as long as you can keep thinning the material you make it fatter for the same weight.
At some point, however, you run into a material strength limit. Hence the old "beer can" syndrome of the super-fat Cannondales. Carbon can't be made as thin as Al can and therefore the optimal tube diameter is lower.