Incidentally, the other non-white versions of sugar, demerara, muscovado, golden caster, etc, are all made by taking white sugar and adding a proportion of the mollasses back in that was taken out when refining.
Incidently, if sulphur dioxide content is a concern, white sugar contains very, very little (a few ppm IIRC - I used to test how much 35 years ago). It all ends up in the mollasses. I suspect some brown sugars have much higher SO2 content than white.
The level is usually <<3ppm SO2 in white sugar. There is a labelling limit of 10ppm, so if it is higher than that it needs to be declared on the label (it is an allergen in EU law). White sugar is not bleached; the SO2 just prevents colour-forming reactions from occurring quite early on in the process. (I have to declare an interest; I work for a sugar company.)
Some browns are made by adding cane molasses to beet white sugars; different versions have different molasses addition rates and different particle sizes. Cane browns of various types are hived off from different parts of the process, but all are white crystals with molasses on the outside. Aside from the differences in colour-forming compounds in the white crystals, there is no appreciable difference between cane & beet=derived sucrose.
As said upthread, honey is a mixture of fructose & glucose, the ratio coming from the various plant nectars collected and which affects whether the honey is clear (a syrup) or set (a slurry of crystals in syrup).
Cane molasses does have a significant amount of sucrose; it's about 45 - 50% by weight. The sugars cannot economically be removed by crystallisation. However, the salts & other compounds from the cane take the edge off the sweetness. Don't try cooking with beet molasses though, unless you are a ruminant & enjoy eating such things.
As far as eating sugars goes, I do, but the delivery system makes a big difference. Soft drinks are too much in one go for me (all glucose & fructose); on the other hand, bananas (which at 12g / 100g have more sugars per unit weight than colas) are absolutely fine.