I guess covering your nose might also keep the smell out, but it doesn't quite accomplish the same goal.
The Japanese have a saying (kusai mono ni wa futa o shiro) which means "if it smells bad, cover it up/put a lid on it." This goes beyond common attempts to cover up ones mistakes or to turn a blind eye to bad behavior as it commonly and casually occurs in American culture. It's about not facing hard truths, discussing serious problems, and willfully remaining oblivious to things which desperately need to be faced. It is not necessarily linked to morality, though it can be, but is a culture-wide squeamishness about confronting unpleasantness on multiple levels. It keeps serious social, economic and political issues from being dealt with and contributes to interpersonal distance between people who have problems, but do no face them.
The culture of "kusai mono ni wa futa o shiro" stands in the way of improving situations and is a roadblock to communication and I won't miss it.