I used to work grid with a woman who pulled just that stunt. It was a long time ago when double layered suits weren't the vogue. She had a couple of drivers that had continuously been a$$holes (long story). Just before the 5 minute warning she had tech announce that there would be an underwear check for all drivers. Everyone complained but complied immediately except for the two offensive drivers. They left the grid and had to get redressed before the one minute warning. They didn't make it, but they never gave her trouble again.

As to the socks, when working grid, one of my people noticed that a fairly young driver of an SM was standing and chatting with the other drivers and was wearing a pretty worn out pair of mesh top athletic shoes with "gym" socks. I had to confront the driver about his gear. His father, standing nearby, jumped down my throat with both feet and told me that it was perfectly safe and that he always drove that way. I politely told him that he wasn't going out on the course until completely dressed appropriately. Much fussing and cursing proceeded on dad's part. Both retreated to the race gear dealer and purchased the proper equipment. Since it was practice, little time was lost.
The boy's father latter apologized to me for being nasty. He said he was only trying to safe money as the kid was growing in sizes daily.

As for checking socks on a driver in a car...I've got too much to do before releasing drivers onto the track. If tech has a bunch of spare people (I doubt it) they can check them. As for their need, yes, they're needed. If you've ever seen a burn patient (from even the smallest burn) going through rehab, you'd agree. However, I hate wearing them while driving. I don't see how they work as they are so thin, but that's not my call.

Pet peeves.... Why, if you have an exposed filler pipe for the fuel, do you have to cover it? The neck, the filler, the vent, and the tank are all of the same guage metal. Yet it has to be covered with either a thin piece of metal, or the stock plastic (i.e. flammable) interior panel. Makes little sense in terms of safety.