It was a dark and stormy night, and the body was right there in front of me. It just didn't know it was dead yet.
Who thinks like that? I know it's a literary contrivance, but my initial question is at its heart all about the narrator's motivations. Why is he/she telling this story?
Well no, it doesn't quite work like that. Consider the sentences in third person:
It was a dark and stormy night, and the body was right there in front of him. It just didn't know it was dead yet.
One word is changed, one pronoun. Is it now a narrative where the pov character is talking to someone mentally or physically or do you see it as just the pov character's thoughts, the third person pov character essentially talking/thinking to himself and processing information? We do, in fact, talk to ourselves internally as if there was another person, or even more than one, which is also ourselves. We do make jokes to ourselves. We keep a running monologue as we process what we are experiencing.
Do I want some more shrimp? That would probably make me sick. Yeah, better not. Shrimp sickness, there's probably a fancy word for that. And so forth. Try recording what goes through your head for an hour. You'll find some interesting conversations and possibly suspect you have ADD.
And in the fictional narrative, there is some contrivance for narrative voice but it is not substantially different in first person than in third. So what you're making a requirement of first person is actually just an option of first person and one of the ways that first person format can be useful for different story approaches.
So there's first person, present tense. That's the running inner monologue of the first person narrator told with immediacy as it happens. Then there's standard first person, past tense, which is still a running inner monologue of events that are currently occurring, but gives the reader a different, less intense rhythm. Most first person is in this form. Then there's first person, past tense, with foreshadowing to imply that these are past events that the first person narrator is recounting. That's the one that is probably giving you some fits. It's used quite often in mysteries, as is straight first person, past tense. It's the "little did I know" version. That version can be interpreted as the first person narrator recounting events to others or as the first person narrator simply remembering to himself what occurred and how it felt at the time. It is, however, not necessarily spelled out which it is and if the former, who the pov character is relating the story to.
Then there are first person formats where the first person narrator is non-omniscient, semi-omniscient or omniscient. In the non-omniscient version, the first person narrator is definitely telling someone the story of past events (or past events up to a point at which the story may then switch to a present timeline,) which occurred to the first person narrator or which the first person narrator was told by someone else. The someone being told the story is usually identified at least as a general person/character listening who may or may not speak, or as a general audience (dear reader.) The first person narrator gives his thoughts and feelings and conclusions about events, and talks about the actions and speech of others, with interpretations of their thoughts, but the first person narrator doesn't know the actual inner thoughts and feelings of other people beyond what they say and has to guess.
A semi-omniscient first person narrator is similar, recounting a story that occurred, perhaps even to multiple generations. The semi-omniscient narrator is told the thoughts and feelings of others by those others, who fill in parts of the stories along with the first person narrator's interpretations. These thoughts and feelings of others are presented as them feeling and thinking them at the time, as if a third person narration, but at the same time are being related through the first person narrator, with commentary to one degree or another by this narrator. An omniscient first person narrator knows the inner thoughts and feelings of all the characters in the stories and presents them as they think and feel them, just like a third person omniscient narrator, without having to mention how the narrator came by the information, was told it.
Then there are first person narrators who are frame story narrators. These narrators are telling a story directly to an audience, possibly characters, such as people in an inn, but possibly just to the general reading audience. But once they begin the story, the story is told in third person, as a mixed format, with the first person narrator framer acting as an omniscient or semi-omniscient narrator but not necessarily present in the story at all.
Then there is revolving first which has multiple first person pov characters who each take a turn controlling the narrative. Revolving first can be done as standard first or a form of overall narrator. It is often done as essentially the same narrative you'd do in third person limited, but in first person. There are also straight mixed formats in which part of the narrative is in third person limited or omniscient and parts are in first person, possibly of one character or more than one character. And lastly there are brief fragments of first person in a narrative that are usually used for emphasis or to represent a dream state, etc. Letters, diaries, etc. are a device that usually reference the past, but not necessarily completely. For instance in a diary entry, just past events will be related but events that occur after the date of the diary entry will not be foreshadowed. These devices can be used in a manner of non-omniscient, semi-omniscient or omniscient formats.
And then there are divided minds where the mind of the first person pov character is literally different people or forcibly divided halves. The first person pov character may be talking to someone or just thinking, but it may be like a conversation -- our inner monologue (which tends to be more of a dialogue) writ large.
For instance, if the narrator is telling their story to someone that has the same knowledge of Quantum Flux Capacitors as they do, then it breaks the fourth-wall believability factor for the narrator to suddenly explain how the Quantum Flux Capacitor works. However, that information might be absolutely vital to the audience's understanding of the story. There are ways around it, but you need to be aware that the issue exists before you can fix it. Just like the issue with Mark VIII Quantum Flux Capacitor. You know the one. If you try to push it up past 1.5 they completely lose their phase encoding and that's when the real trouble begins.
If I am thinking to myself, I may mentally review how the Flux Capacitor works. I may remind myself that if I try to push it up past 1.5, it will completely lose the phrase encoding and that will be where the real trouble begins. I may or may not think about what that real trouble is.
If I do have a first person pov character talking to someone, a character, then that character on the receiving end is there because I want him and have a specific purpose for him being there in that scene re information I'm conveying for the readers. If I'm having the first person character recount to the audience, I have a choice of treating the audience as not knowing what the Capacitor is or knowing, but reminding the audience. And yes, it's contrived, but the majority of the audience accepts it as the style of the story. A percentage will not like that style but a percentage always doesn't like whatever style and format you pick.
I think that authors do analyze how they want to do it. But the claim that first person is always an accounting to another, but third person is not doesn't work for all the approaches.