The problem with antioxidant supplements is that they don't necessarily work well with metabolism.
After the antioxidant hype and supplement boom yielded no health benefits, there have been multiple large studies showing no effect or negative effects. They can remove benefits from physical exercise and increase cancer risk. Vitamin C can remove benefits from exercise.
Overall the risks and benefits are small, but basically they are all useless. If studies show benefits, it can be because some of the subjects suffered from deficiency. You should take them only to treat vitamin deficiency or increased need. Taking more and more of the good stuff is not automatically better.