The strongest thing coming from your feet shouldn’t be the odor. It should be the power you need to do better lifts. And by putting your bare feet on the floor, you can increase your strength on one of the all-time best muscle-building exercises: the deadlift.
Going shoeless decreases the distance you have to lift the bar. A few millimeters might not seem like much, but it will give you a significant mechanical advantage—especially if you’re used to lifting in a shoe with a squishy sole, which reduces your stability—and, therefore, your strength.
If your gym won’t let you lift in socks—a stupid rule that doesn’t improve safety (as if shoes would protect your toes if you dropped a plate on them)—use the most minimalist footwear you can, like a Sockwa G4, Vibram FiveFingers, or even some Converse Chuck Taylors. Your old high school wrestling shoes will work, too.