Some antioxidants (such as certain vitamins) are known to be lipid soluble and therefore prone to accumulation and subsequently become toxic since they can't be excreted as quickly as water soluble compounds. So why would anyone want to flood an organism with them? Derivatives of vitamin A are known to serve as hormones which end up involved in regulating gene transcription. Things are never as simple as they seem, which seems to be a point that is overlooked.
Also, this interest in somehow quenching all oxidative chemistry in the cell is getting a little odd. We oxidize carbohydrates and fats in our cells for energy. We oxidize foreign substances to ultimately aid in us excreting them. We oxidize various unreactive compounds in our cells to subsequently functionalize them with new chemical moieties. There are entire journals dedicated to free radicals in chemistry and biology, both their important roles and their damaging effects. The NIH link to free books I shared earlier is a resource you should be focused on fully exploiting - there's solid material in genetics, molecular & cell biology, and biochemistry that should be worked through before trying to tackle the immense research literature out there in DNA repair, free radicals in biology, and the like.
I really don't have anything else knowledgeable to say about any of these topics at this point.