I think antioxidant has too much importance placed on it, especially from a marketing point of view, it’s something that can be easily marketed. You can get it from eating vegetables, herbs and sprouts, it is not necessary to eat lots of fruits, which will raise your blood sugar and too much will ferment longer in your body. (For that reason, some recommend to eat fruits alone on an empty stomach and not with a big meal.)
In the book Fat for Fuel, Dr.Mercola talks about why too much antioxidant isn’t actually a good thing as it “indiscriminately lower the important biological signaling function of reactive oxygen species”. Also antioxidant aid the survival of cancer cell (suggested by James Watson). The idea is to reduce free radical instead, and this is through the ketogenic diet.
He also talks about the the idea that it’s not healthy to be permanently on keto which I agree with. You want to step out and eat a bit more healthy carb, such as on days you’re doing more activities and work out.
Some people here are against it all, and that’s fine, but when I’m at a healthy weight and with a good fasting blood sugar, I don’t see the problem with having some healthy carbs periodically. Go for lower glycemic fruits that have more fiber, like wild blueberries, grapefruit and maybe sweet potatoes. As for coconut, if you open up your own, eat the meat too, or drink the water while you exercise. I honestly don’t think there is anything wrong with having a fruit once a while, but you have to be careful as it can pull you right into being a fruit binger if not careful.
If you look at the Ayurveda medicine perspective, they eat foods by season, and fruit isn’t something that should be available to you all years round.