I’ll go first. After your turn the water off in the shower but before you get out, use your hands to wipe off any standing water on your body. Maybe even give your legs a bit of a shake. This way, you won’t drip nearly as much when you get out, keeping the floor and your towel drier.
Utensils will get dried eventually when upside down and you’ll have to wash them within few minutes or wetting utensils would be of no use.
Yes, they will dry up eventually but not within a few minutes, that’s just not true. My tip was meant for people who still plan to wash their dishes within a reasonable amount of time. I wouldn’t be doing this myself if it wasn’t useful.