I switched a drop bar road bike to bullhorns, ones that angled out and up a good way. I agree with everyone that the bike stability is unaffected, but with my hands a good half foot (or more) farther out, the bike's response to handle bar input changed dramatically. One inattentive twitch of the bars practically puts the bike down.

This is on a bike I've ridden for over 30 years.

Recumbent riders call this the tiller effect

Sort of becomes a semantic argument about what one means by the word "handling". Getting your grip points farther out from the headset unquestionably affects the bikes response. Is that handling?