I'm trying to understand what させてもらう really means, beyond different translations I have seen, since they don't always seem to work.
I found this question, which gives as meanings "[decide to] take the liberty of" and "someone allowed me to", but they not always works.
For example, "take the liberty to" doesn't seem to work in sentences like this (from Gamers!):
with a boy speaking about his girlfriend, which is the top girl in his school under every aspect, sounds kinda strange: "I'm happy since I'm taking the liberty to date her"? "Someone allowed me to" sounds better, like "I'm happy she is allowing me to date her".
Then there are sentences like this (from Kakegurui Twin):
where two girls are competing by gambling on who gets to use the library (賭場 because it's also used as gambling den); in this case, 「勝たせてもらう」 as "You will allow me to win" sounds strange, while "I'll take the liberty to win" sounds better. The sub is "I'm gonna win", which sounds even better.
I get that させてもらう is causative + もらう, so "someone allowed/made me to" + "to get someone to do something", so I think it's like "to get someone to let/make me do something"; but this literal meaning is kinda strange, since "I'll get you to let me win" doesn't really sounds right, since the opponent doesn't let her win, rather she plan to win despite her opponent's wishes.
Given the meanings I found, some of them seems to always fit the various situations, but I was wondering if there is an underlying meaning to all of them, maybe just some form of politeness like the previous examples literally meaning "I got her to let me date her" and "I'll make you let me win" as less direct forms than "She dates me" and "I'll win"; or if it really has different nuances ("to take the liberty" vs "to be allowed to" vs "to do something") depending on the context.