Because keeping your mouth clean is both cheap and easy. If there’s a minuscule chance that it will reduce any risk in cancer, why not? Besides, who wants bad breath?
Because we don’t know either way. There’s also a minuscule chance that doing extra cleaning might lead to the opposite effect, as evidenced by another reply here. We don’t know. This article mentions nothing about halitosis.
Yes, but it’s so cheap and easy to do both time-wise and cost wise that it’s a completely moot point.