Those whose jobs need them to stand or walk around for lengthy periods of time should realise the importance of wearing protective footwear and socks. This is a very important aspect of your company's health and safety policy.
No one suggests stepping barefoot on sharp metal or glass. Because of how terrible it is, you have no desire to try it out. Accordingly, you should expect your company to enforce clothing standards suitable to the workplace. Wear shoes and socks that are intended to keep you safe from danger while working.