I keep my phone in my back pocket, so yeah if I sit down it's under my butt. I'm also a woman, so my front/side pockets aren't big enough to hold a phone

Every rollercoaster I've been on has a spot for putting down anything you're carrying. It's usually just a cubby, and on coasters with more than one train they're labeled by train so the ride attendant can at least stop people from taking stuff from the wrong train's cubbies. It's obviously not 100% secure, but I think it's rare for stuff to go missing from there, I've certainly never had anything stolen, nor have I heard any stories from friends of it happening.

People shouldn't have their phones in their hands, yes. Nothing wrong with having it in their pocket on a sit down roller coaster though, as it's safely trapped under the rider's butt. Also smart watches can have the same feature, and I know I don't take my watch off to ride rollercoasters.