Why can't the molecularity be determined from the rate law?
The coefficients only correspond to the rate law coefficients if the reaction is elementary. Elementary reactions are ones where the reagent(s) combine through a mechanism implied by the reaction. These are simple. Many reactions aren't as simple and have multiple steps. 

Check out this link, example two. The reaction is actually comprised of two reactions where the slow step determines the rate coefficients.

As you can see, you cannot just read the equation and get the coefficients. One can only determine whether a reaction is elementary (i.e. find its rate law coefficients) by experimentation.