The only answer I can really offer is that in those parts of the (developed) world where bidets are not common, society functions just fine and doesn't seem to be negatively impacted in any way by their absence. I don't have a bidet and I don't always shower immediately after doing my business. Am I "potentially walking around with poop and paper caked in my butt crack all day"? I guess, technically, yes. But it's not something I've ever noticed and it's certainly not something anyone else has ever noticed.