Most introductory texts on analysis begin by studying the properties of the real line and (either by hypothesis or construction) assert that $\mathbb{R}$ is a complete and totally ordered field. All of analysis then seems to flow from these precepts. On the other hand, metric spaces themselves can be complete and totally ordered and for higher-dimensional developments one can consider Banach spaces. So, other than for motivational and pedagogical reasons, is there any need to actually develop analysis in the context of $\mathbb{R}$/ $\mathbb{R}^n$ instead of complete metric/Banach spaces? Are there results that are unique to $\mathbb{R}$/$\mathbb{R}^n$ that cannot be developed in complete metric/Banach spaces? Of course, everything that is true about these abstract spaces is true about $\mathbb{R}$/ $\mathbb{R}^n$ but does the converse hold?
Update: Since asking this question, I have found a reference that gives a really nice comparison between metric/normed spaces and $\mathbb{R}^n$. It's found on pages 150 - 152 in Marsden's Elementary Classical Analysis (1st Ed). Although the text itself does not develop everything with full generality (hence the title Classical Analysis!), the charts on these pages list the results in the text and indicate whether they hold in abstract spaces and indicates what restrictions need to be placed on a space for a given result to be valid.