As an American myself who lives with a British educated partner, we have discussions like this on a regular basis.
Before I get to my point of view on the question, I would like to point out that the Quora link you provided answers this question:
Used as a verb, the word "request" is only a small step back from "demand." In fact, it is a demand (Quora link)
To be more general here, as I have observed, Americans' usage of the English language is far less formal than the UK, most apparent in business situations and formal (nonlegal) documentation. In this sense I would venture to say that Americans see formality in an entire different perspective than our British counterparts. Whereas formality may be in line with British social structure and therefore polite, we on the other side see formality as distant and therefore unfriendly. Consequently, adding small bit of casualness is seen as more friendly and therefore more polite.
"Request" - an act of asking politely or formally for something (google defined)
Given what I just mentioned and what the Quora link states, the usage of "request" is not only direct and demanding, but overtly formal in an American’s eye, giving the word a double "no no" for US culture. So how do we Americans "request" for something? Request implies "to ask". Americans just ask. Less formal? Yes. More polite? Also yes.
The alternative for "Request" in US English: "Could"
"Could you do this and this?" etc, instead of "I request (that) you do this and this."
However, let’s say you must use the word "Request". Changing the word to its noun form "I sent a request...", adding polite redundancies, "I humbly request...", or phrasing it in a question (though redundant), "Could I request..." are the more polite American alternatives.
I hope this answers your question, and gives you a better understanding of the differences of British English and American English.