Given its nature as an LMM and a complex next word predictor, the phrase "it is important to remember" could be a way that was inadvertently trained so that it keeps itself on track.
If it has "some points, it is important to remember {something}, some more things" it may be able to better generate text compared to "some points, weird tangent".
Since it doesn't have a hidden memory, everything that it "thinks" is out there in the text including its own cues for what it should do. It also can't go back an edit its previous text to remove the self hints or clarify earlier points without calling them out. That style of writing differs from natural human writing since we are able to keep on topic (or not) without needing to write messages to ourselves that others can read.
When we do, it's pointed out rather than trying to slip it in casually. "Note to self or reader" for things that are to be pointed out and break the flow of the text or "as an aside" for the tangents.