|Can we discuss this like civilized people?|
Some of this confusion results from the misunderstanding of skill checks in general, but much of it is related to how powerful Persuasion can be when used. To clarify, let's start with skill checks in general. A skill check is just a special kind of ability check that allows the PC to add their proficiency bonus if they are proficient in that skill. Here are the Rules as Written in regards to ability checks.