The reason why I think that there are very few bathrooms is because Nintendo want to be mature. I'm quite sure we don't need to see Link emptying his bowels during the quest or look at someone else doing the same. It was an E-rated game (exception: TP), and I'm sure they don't want crap jokes. Now, if you're thinking of why the regions didn't have restrooms, that's a different story.
Outhouses weren't that common way back then. If I remember correctly, castles (while they had a sewage system) weren't the cleanest. In ancient Rome, there was a place where you could go to relieve yourself, which was then hooked up to the ancient Roman sewage system. I'm quite sure they wouldn't want to pollute Zora River because of the pact that both the Hylians and Zoras have. I'd think that it would involve a nice hole in the ground and a shovel if there isn't a public outhouse already there.
There are a number of reasons you could throw out, but remember, the developers don't want to throw in defecation jokes...that would just make just about every game E10 or T for crude humor. If you're looking into fan theory, then there's a lot of reasons you could throw out there.