Why do we need Lebesgue to claim that the length of $\mathbb Q$ is $0$? Since we know that $\mathbb Q=\bigcup_{n\in\mathbb N}\{x_n\}$ (i.e. it's countable), why do we need Lebesgue to say that $\mathbb Q$ has length $0$ ? Indeed, if $$\operatorname{Length}(\mathbb Q)=\sum_{k\in\mathbb N}\operatorname{Length}(\{x_i\})=0,$$
since $\operatorname{Length}\{x_i\}=0$. So if this is not valid, how should the length of a set be defined?

What you are saying is that Lebesgue's definition of measure (or length, if you insist) is obvious. Yes, it is, in retrospect! But Lebesgue was the first to define it explicitly.
