When you add "Please" to a request, it makes that request less of an order. The word is there because part of being civil is not ordering people around abruptly. (Even if you have the authority to give them tasks.) So in fact, when it is used for civility, it does mean "I beg you". Or at least, "I softly order you".

So in fact it doesn't make sense in some circumstances (though those circumstances are narrower and fewer than fubu seems to think).

For instance, "please" is clearly out of place in "please put the gun down on the pavement, or I will shoot!".

The civility-conveying meaning of the word is out of place in abrasive speech; for instance it is out of place in "please get off the f___ing road!" In abrasive language, if "please" appears, its presence is ironic. For instance, in a sentence like "please don't start with that bullshit again!", "please" doesn't have any connection to being civil; it doesn't function that way. Other such politeness words are also ironic in abrasive speech. "Kindly keep your mutt off my lawn!"

(There is even the usage of the word "please" by itself, or nearly so: "Oh, please!" or its variant "Puh-lease!" which expresses disagreement or disapproval.)

You made a very accurate description, though I'd argue that depending on situation and culture, "please" in "please put the gun down on the pavement, or I will shoot!" might not be that much out of place.

It conveys friendliness, the concept of "we're all friends here and we don't want anyone to get hurt, so let us sort this out without a mess"[0]. On the other hand one could argue that abrasive speech is very effective at bypasing various psychological bareers and delivering message straight to the target - after all, that's the reason for so much shouting and insults in the military. So there's a trade-off.

[0] - I guess I might have been watching too much Star Trek in my childhood, which gave me a deeply ingraned attitude that we can all see the bigger picture if we try hard enough.