Since wider tires do not have same traction per sq. in. of
footprint...
False, a common misconception. If the tires are inflated equally, the footprint is
exactly the same area (square inches or square cm). Think of the meaning of PSI as "pounds per square inch" and you'll get it. Roughly 3000 pounds with driver and gear, divided by 4 is 750 pounds per tire, divided by 33 psi is 22.7 square inches per tire. Consider weight distribution and perhaps the front tires have more like 27 square inches and the rears 18 square inches, but you get the point.
It's the SHAPE of the contact patch that matters.
A short and wide contac tpatch, as a wider tire would provide, typically gives better lateral traction to a point, the similar fore-and-aft traction, a greater tendency to hydroplane, and more "instantaneous" steering feel, and perhaps a tendency to tramline on uneven pavement.
A long-and-narrow contact patch gives less lateral traction (the tire rolls onto its sidewalls more), better on-center steering feel, a more progressive breakaway (hence less
precise steering feel), better traction in wet/slush/snow, and less tramlining.
Your point, however, is valid, depending on how you define "better handling". Relatively narrow tires are more comfortable handling tires, and wider/low profile tires have their drawbacks in the "comfort" department, but can provide better lateral grip (in general) due to a wider contact patch, and a more immediate steering feel.