YSK this is actually a bad idea. By repeatedly damaging the skin this way you can actually trigger a nerve condition where the ends of your nerves just send pain signals all the time. People who work in professions where they scrub their hands a lot for their work are at risk of this. It's probably fine to do every once in a while, but don't make it a regular thing.

The chance is small, but I know a few folk who were real men when they were younger so they didn't wear gloves when they really should have. Just don't worry about it and scrub it off was the mindset back then and men wearing PPE were (and sometime are) seen as weak. But they describe the pain as getting stabbed in the hand repeatedly and wish they just wore the gloves.