As someone that grew up hating socks (parents only bought the ones with a thick seam at the toe), yes, the requirement to wear socks is a social construct. There are other ways to avoid smelly feet.
Currently, I wear shoes with washable insoles and I have multiple sets of these insoles. I also rotate between shoes, and these shoes can also go in the wash.
I do wear (nice, seamless) socks when I go hiking, but for day-to-day at the office they're unnecessary.