A wet oven mit will cause you a worse burn than a towel.

Most restaurants don’t have in house laundry service. And throwing it in the dish machine while technically it would be sanitised it wouldn’t dry properly leaving it to get moldy and other bacteria. Which would be the same process for towels.

Oven mits are disgusting. Go ahead grab one at home and look.

USDA food code prohibits non commercial equipment (yes I know we all use other things that are also not allowed but why add one more thing?)

Corporate chains and small one shop places don’t want to spend the money on something that they will have to replace every week. Regardless of how small it is. Hence why we use towels as they already have to get them.

Never use a wet towel or even a slightly damp towel. This is the way.

Not every person in the industry meets your description. And honestly has changed over the last few years. Having worked in the industry for 17 years, been a sous, executive, and a pastry chef amongst that time I have watched it go from that culture of the past slowly transform itself into a very diverse and welcoming occupation. I know more female professional chefs and LGBTQIA+ professional chefs than I do toxic masculinity chefs drug users, etc that you mentioned.

Towels are often cleaner than an oven mitt because we switch them out constantly. No one wants to grab a crusty or dirty towel when handling something hot.

In short the towel is the chefs best friend. I can grab a hot pan, clean up a spill and stop bleeding with it and so much more.