Ramban describes the purpose of the book of Deuteronomy in his introduction to it:
יבאר בו משה רבינו לדור הנכנס בארץ רוב מצות התורה הצריכות לישראל ולא
יזכיר בו דבר בתורת כהנים...שכבר ביאר אות' להם והכהנים זריזים הם לא
יצטרכו לאזהרה אחר אזהרה אבל בישראל יחזיר המצות הנוהגות בהם פעם להוסיף
בהם ביאור ופעם שלא יחזיר אות' רק להזהיר את ישראל ברוב אזהרות...ועוד
יוסיף...כמה מצות שלא נזכרו כלל כגון היבום...אבל לא נכתבו המצות בספרי'
הראשוני' שידבר עם יוצאי מצרים כי אולי לא נהגו באותן המצות רק בארץ אף
על פי שהן חובת הגוף...או מפני שאינן תדירות לא הזכיר רק בבנים נוחלי הארץ
In the book of Deuteronomy, Moshe explained for the generation entering the land [of Israel] most of the commandments necessary for Israel and he didn't mention matters from Leviticus...for he already explained it to them, and the Kohanim were alacritous and dint require additional instructions after they were already instructed. But for the Jews, he repeated the mitsvot relevant to them, sometimes to add more clarification, and sometimes to caution them through a repetition of warnings...and he also added several mitsvot that were not previously mentioned at all, such as yibbum...[And Moshe was told them earlier] But they weren't written in the earlier books addressing the Egyptian emigres, since maybe they only practiced those mitsvot in the land [of Israel], although they are personal obligations [rather than obligations intrinsically dependent on the land]...Or because they weren't common[ly practised] it only mentioned them earlier in the context of those who would enter the land.
Ramban seems to be lumping together two issues: the order that Moshe conveyed different messages, and the nature and purpose of different books of Tanakh. Perhaps this conflation indicates that his general assumption is that the two are intertwined; if for whatever reason Moshe presented certain teachings later; whether as clarification of existing laws, as exhortations to keep existing laws, or as introduction of new laws, if now was when he taught it, then the place for it is Deuteronomy. The question of why include the whole book if it does not introduce new laws, however, doesn't exist in this scheme, for besides for the useful exhortations, he himself notes the existence of new legal information.
In his last line, however, he considers the possibility that the commandments in Deuteronomy were actually instructed earlier, but not mentioned since they arent frequently practised. Accordingly, their placement in Deuteronomy is not the natural result of when they were commanded as he assumed until now. Rather it relates to the role of the Deuteronomy. Apparently, (and I stress that this line at the end of the introduction is only parenthetical, and seems to be developing a new approach to the nature of the work) Deuteronomy is a secondary work, to the primary legal books, and information that is not practiced as frequently is to be "dumped" there.
Importantly, Ramban seems to have no problem with the fact that passages that don't contain new legal information would be included in the Torah. This is perfectly consistent with his sentiments in Genesis (1:1) in which he rejects the (implication of the simple reading of) epic Rashi. There he is astonished at the idea that the Torah should have begun with the legal portion - after all, the creation narrative is central to the Jewish faith! Rather, he explains away that idea as emphasising not the central nature of strictly legal passages, as a reason to skip to them, but rather as emphasising the esoteric nature of the creation narrative as a reason to skip over them, and settle for the summary in the Decalogue stating that God created the world in six days, and rested on the seventh.
In summary: his first (and apparently primary approach) is that those mitsvot mentioned only in Deuteronomy wouldn't just be mentioned in earlier works, since that would be anachronistic. His second approach is that it could've theoretically been mentioned earlier, as it was already binding, but infrequently practised laws are relegated to Deuteronomy. Regarding the inclusion of passages that do not introduce new laws, Ramban does not seem bothered, likely because he never advanced that strictly legal-only vision of the Torah, in the first place.