re:Is it for the same reason that many animals dig holes to hide their excrement?

From what i read, it more likely for preditors to bury their excrement than prey-- and this goes right down to incects. Large wolf spiders eat small wolf spiders.. and when small wolf spiders are exposed to the smell of excretia from large wolf spiders that have been eating smaller ones.. the smaller ones behave differently.. (than when exposed to the smell of large wolf spiders that have been eating other bugs.) they hid more..

what is taboo changes from culture to culture.. in the past-- "out house's" were sometime 2 or 3 seaters.. and there are public toilets in various places that offer less than 'western' privacy.. some rather "civilized" cultures have no problem with (men especially) urinating in public. In most of the US this would get you a citation for public indecency-- and maybe a second for urinating (pollution) in public.

I have been to bars (gay bars) were the stalls in the toilet had no doors-- and the facility was unisex-- (the idea was the guys weren't much interested in looking at the gals anyway...)