Europeans would absolutely eat sugar in the same volumes if it were as cheap there as it is in America. As with most of the cultural differences between the regions, a lot of it comes down to economics: if gas were cheap in Europe, they'd also drive big SUVs; if land were as cheap in Europe, they'd have McMansions; etc.
£0.65/kg in Tesco in the UK, 7.5kr/kg ($1.20) in Føtex in Denmark, but $1.80/kg at Walmart. Corn syrup at Walmart is more expensive, $2 a pint, but presumably cheaper in bulk packaging. (Last time I was in the USA, I saw an entire freight train of tank cars full of HFCS.)
(You'll also note that plenty of rich Europeans prefer large "normal" cars, like Audis, BMWs, Mercedes etc, and a nice apartment in the middle of a city.)
The southern US used to produce a lot of sugar. Before refrigeration it was heavily used as a preservative.
So there's a big market that expects things to have a lot of sugar in them.