The importance of Rolle's theorem lies in the fact that it's used to prove the mean value theorem, which is a central result of analysis, eventually leading to the fundamental theorem of calculus. But if I compare the usual proof of the mean value theorem to other typical proofs, I come to the conclusion that the theory is built up differently than usual. A typical proof in analysis might start off with: "Without loss of generality, assume $f(0)=0$, otherwise consider $f(x)-f(0)$", or similar statements. The mean value theorem could go exactly the same way: "without loss of generality, assume $f(a)=f(b)$, otherwise consider $f(x)-(x-a)\frac{f(b)-f(a)}{b-a}$", and then we'd just use the proof of Rolle's theorem.
But in the "canonical" development of analysis, Rolle's theorem gets to be its own theorem, instead of just being part of the proof of the mean value theorem. Why is that? Does it have any other significant applications I'm unaware of? For instance, the special case of the identity theorem in complex analysis which says that zeros of holomorphic functions $\neq0$ are isolated is important on its own because it's used in treating isolated singularities of fractions of holomorphic functions. This makes it a reasonable thing to declare as a theorem of its own, even though it could also be a lemma on the way to the identity theorem. I don't know of any such important application of Rolle's theorem. Or is it a pedagogical choice, aiming to make the structure of the argument for the MVT clearer? Any other possible, maybe historical reasons?