My sense as a native speaker of English is that "Give me an example of this" can be a perfectly polite request in English as well. In both languages, adding "please" to the sentence would make it more clearly a polite request.
A slight modification to wisty's example would be if you're at a restaurant and the vinegar is at someone else's table. "Give me the vinegar/给我醋(把)" is equally polite to something in English like "Please would you pass the vinegar" which you might be more likely to say to a complete stranger. It's definitely minor, but creates a feeling of convenience which builds over time: terseness as convenience instead of rudeness.
Another example might be getting a stranger's attention to ask a question (again, something common to my experience if not the most varied example). In English it's "Hi, would you mind helping me?" "Hi, could you answer a question of mine?" "Hi, I have a question..." In Chinese it's just "please (let me) ask/请问". The "let me" is parenthetical to make it sensible in English, but it's not required to enunciate it (请让我问你）.
There is zero conjugation, a noun, the action most closely associated with it, and the verb which generates that noun might all be the exact same word with the meaning derived by context or (if ambiguous) helping words -- especially when speaking. People strive to speak chronologically so that "He took the train to the city" makes sense but "He arrived in the city by train" is strained. The 了 particle is so overloaded as to have many different, non-overlapping contextual meanings.
You might say that Chinese is structured more by convention than boilerplate, but that's at best a weak metaphor with a lot of connotations which I don't think carry to human languages well.
I don't know, but I guess my follow-up question to your factual statement would be, "Do you have any examples attested by professional linguists who have carefully compared languages, or is this based on your personal experience?" The reason I would ask that way, which I hope doesn't sound impolite, is that my experience is to the contrary. I find English to be a rather informal language among the dozen or so languages I have studied most closely.