There are pitfalls in doing so. I think the main reason people without an allergy feel so good on a gluten-free diet is that they are giving up all the refined-flour foods that dump staggering amounts of inflammation into your body and make you feel just terrible. This is a good reason to avoid gluten. But gluten-free muffins, pizza, and bread are often even less healthy than their gluten counterparts.
Just look at the ingredients on a box of gluten-free pizza: modified rice starch, rice flour, brown rice flour, potato starch, potato flour, evaporated cane sugar. For blood sugar alone, these ingredients are far worse than what goes into your average whole-wheat pie. This is one reason nutritionists worry that a gluten-free diet can leave you deficient in fiber, iron, folate, niacin, thiamin, calcium, vitamin B12, magnesium, and zinc – all common in whole grains. It's also why I try to avoid inflammatory gluten, like white flour, but still get a daily dose of whole grains like barley, whole wheat, and bulgur. That said, I do often enjoy oats, quinoa, amaranth, and chia – all naturally gluten-free.