Tooth decay is purely caused by diet.
Certain grains also cause it, not only sugar.
Rice for example is very bad for teeth (90% of people damaged teeth, acidic starch is what they assume), while potatoes are much less harmful (~10% if I remember correctly, since potato starch is alkaline).
Sodas (anything with low ph) is terrible for the teeths as it seems.
So it's also not "just carbs", but there are other factors.
So "painting teeth" with dubious chemicals is moronic since the problem is the food. If the food destroys your teeth so much, think what it does on the inside of you which you cannot see.
Eg check out this study: TOOTH DECAY IN RELATION TO DIET AND GENERAL HEALTH NILS P. LARSEN, M.D