I run really wide Nitto's, they're labeled 46 but at the tips they're closer to 48. But that bike is a combination road / trail / cross bike so there are times at slow speed when the leverage helps.

My hands are definitely the widest part of my body on those - and I can feel it when the wind hits.

On my "road-only" bike I run 44's; they are still pretty wide but I have broad shoulders so my hands are in line. But yeah, back in the day, 38 was standard.

One factor that affects handling, is bar height. Think about the relationship / angle between your hands on the drops, and the front tire contact patch. As a bar gets wider or lower, that angle gets wider. I don't have the math/phyics to describe it properly, but you can definitely feel it.