Privacy's definitely important for anybody, it isn't very fair (not to mention kind of rude) to make people publicize every little thing that they're doing. Plus people sometimes just need "alone time," not in what I'm sure people are assuming, but if they just want to take a nap or have some quiet so they can read.
I wasn't allowed to close the door to my room, let alone lock it. I'm also an only child so this was only when I was at my dad's house with my stepbrother, who closed his door all the time. I really only closed it if I was playing the radio and didn't want it to be too loud for other people in the house, but beyond that, there wasn't a lot for me to hide as a preteen. Sometimes I just liked having the privacy though, even if I was just doing homework and didn't want to be bothered.
Nowadays I don't spend a lot of time in my room, as all of the space I use to work (whether it's my computer or larger projects) is out in the living/dining room. I only use my room to get dressed, sleep, watch movies or play console games, and in most of those cases I keep the door closed. My mom doesn't have to drop off laundry or anything for a few reasons, the most obvious being that my room is literally right next to the washer and dryer, so it's useless for her to pick up something of mine, turn 180 degrees, and knock on my door.