Bosh, piffle, and nonsense that.
You can write it that way, if you want; the conventions of writing let you get away with it. But if you have ever read C. S. Lewis's Till We Have Faces, you know it opens with the narrator observing that she hopes her book, when completed, will make its way to Greece, where (she has heard) men are willing to question even the gods.
First person, unlike third-person limited, allows the writer to take into consideration who this story is (allegedly) being told to, and why, and where, and whether in writing or by the spoken voice. In extreme cases of the spoken voice, the writer gives us a framing story that tells us the entire setting; in extreme cases of the written voice, the work can shade into epistolary novel, constructed of documents. Or some of them. You can get away with alluding to only some of these considerations. (On the whole, unless you include something to show that the narrator is consciously telling a tale, I find that the unreliable narrator is a base trick; if it looks like a third-person-limited with the pronouns changed, it would appear to be as honest as that.)
On the whole, what first-person is most like is omniscient. In both cases, the narrator can (though does not have to) be as chatty as you please. In both, therefore, voice can be of utmost importance, drawing the reader along through the story to hear more of what this engaging voice has to say even if the plot does not keep you on the edge of your seat. In both, you can get away with considerably more info-dumping than in third-person limited; Robin McKinley's Beauty opens with info-dumping, but because Beauty's voice catches us, we read on.
Not entirely like. True, the conventions of the field allow us to suspend disbelief in prodigies of memory and honesty to trust the tale, but in first-person, we have to be convinced that the narrator would tell the tale like it's being told -- even in third-person limited with the pronouns told. And there is always the question of what the narrator is saying about himself. The (one) Jeeves story from Jeeves's POV and the (few) Sherlock Holmes stories from Holmes's POV are insufferable, because their feats are such as no one could tell about himself and not seem boastful. And in first-person, you can get away with omitting information that the omniscient narrator would have to include because the character wouldn't say such things.