You can live in perfect health on close to zero fat intake. Sustained zero sugar/carb intake is extremely stressful for the body and sends catecholamine levels way up, accelerating aging.
The anti sugar thinking is basically some dumb ideas from diabetes research extrapolated out. If you have a healthy pancreas there is zero reason not to get a load of your calories from sugar. You just have to get sufficient mineral and vitamin intake as well, so for this reason fruit juice is better than white sugar.