When I've rented cars with electronic door poppers instead of conventional door handles, I've found them annoying. Do many people actually prefer them?

Purely mechanical flush exterior door handles are possible if aerodynamics (or giving the impression of trying too hard to be aerodynamic) are a factor. Aircraft have used them for decades. Several older cars have used them including the Chevrolet Corvette (third generation), Subaru XT, Fiat Barchetta, and Pontiac Grand Prix (third generation).