I've cut the added sugar in my diet significantly in the last nine months and had significant, noticeable health benefits. But that's just anecdotal. There's plenty of sound research on this topic also.
One mistake people make is cutting as much sugar out of their diet as possible, even natural, nutrient rich ones from fruit or dairy. Whilst too much of these can also be bad for you - just as most things in excess - cutting them completely can be counterproductive.
White sugar, as you point out, is harmful. And since there are plenty of natural sources of sugar out there, it is also unnecessary.