In the answer to this question I asked (When to use である vs であります?), sazarando responded by saying that "である" is formal but not polite, and "です" is polite but not formal. I sort of understand the distinction he was making, but from my English perspective, I suppose I don't understand why you would want to be formal and not polite at the same time.
The example he gave for である was
A politician giving a speech on TV:
我々は日本国民である - We are Japanese citizens
In this example, why would the politician not want to be polite to the people to whom he is speaking? I understand why you would not use である when talking to, say, a superior at work, because that's simply a private conversation where you need to be respectful to your superior. But in the above case where you're speaking in public or writing in a newspaper or something, I don't understand why you wouldn't be polite as well as formal.
Also as a side question, in some academic presentations I've witnessed, the presenter simply uses 謙譲語, rather than using formal speech, so they would end sentences with でございます rather than であります or である. What would be the explanation for this?