Seriously people, use the fucking fan. It clears away odors and covers up the sounds of your dropping a deuce. If you want to stew in your shit smell and revel in the music of your magical poop plops, do so in the comfort of your own home. If you’re a guest and the bathroom has a fan, turn it on. We don’t want to share.
I always run the fan for the same reasons (and prefer a noisier fan) but it doesn’t actually cover the sound outside the bathroom. It just gives you the impression that it does.