Cameras are more durable than you think! As long as you can tolerate some scratches and you don't drop it, you probably don't need a case.
I've used my small waterproof Panasonic camera canyoneering and caving, and in canyons I just keep it in a cargo pants pocket. It got pressed between me and rocks a few times, and there are some scratches on the metal body from rocks, but the lens is recessed, so it's fine. I can't remember if I have a screen protector on it, but it's a good idea. The biggest issue in canyons is sand getting stuck in the buttons and the lens being wet and foggy all the time with nothing dry available to clean it off.
I've brought my DSLR caving, and it needs a bit of protection for that. I use a lightly padded case and a dry bag since it's not weather sealed. I avoid throwing my pack when the camera is in it, but it still bumps into stuff sometimes in caves.
When I bring my DSLR backpacking I don't bring a case. I just put it in my pack with soft stuff around it. If I bring extra lenses I might keep them in beer koozies, but that's probably not even necessary. I have a screen protector on it, but the screen also folds back when not in use so it's completely covered.
Of course, my DSLR is only worth about $300, and my lenses are worth $100-$400 each, so it wouldn't be catastrophic if something was damaged. I'm looking for an excuse to upgrade, anyway. The most likely ways I can think of that a DSLR would be damaged are getting water in it or dropping it such that the lens mount bends. Most high-end lenses have replaceable lens mounts, anyway, and the cheaper kit lenses might as well be disposable because the cost to repair is about the same as the cost of a new lens.
Depending on your needs a good smart phone (mid or high end from the past few years) might be enough. My waterproof camera is a slight step up from a cell phone, and it's really small and rugged. It takes great pictures, but not professional quality. The only thing I don't like about it is that it misses focus sometimes, for no apparent reason. It's dense because it's mostly made of metal, but it's probably not that heavy.
A good option it to buy slightly older stuff used to save money. I think I've bought all my cameras used or refurbished. If it comes pre-scratched that's even better because you save more money and you don't have to care about protecting it as much.