On the solution to stochastic differential equations and Ito's lemma

Question

In this article, Sussmann shows there is a simple link between SDE of the form $$\tag{1} \mathrm{d}x=f(x)\mathrm{d}t+g(x)\mathrm{d}w $$ and their correspondent ODE, provided $f$ and $g$ satisfies some regularity conditions. But then...what is Ito lemma good for, if every SDE of this form can be solved with the same method as any other ODE?

Answer 1

The article doesn't discuss time-dependent coefficients

$$\mathrm{d}x=f(t,x)\mathrm{d}t+g(t,x)\mathrm{d}w,$$

where Itô-lemma applies.