There are two main reasons people will usually tell you to level everything.

First, cross-class skills. Wile slightly less important with the SB and ShB changes, some of the skills are still amazing, especially at lower levels when you have less CP and no access to the stronger skills or better gear.

Second, being able to craft thing besides just the completed items. Like Frizze said, crafting often requires materials made by other classes. Leather needs a lot of cloth, and vise versa. Armorer sometimes needs goldsmith exclusive ingots. If you want to craft a bed your carpenter is going to need not just lumber, but also metal and cloth. And the list goes on. There's a huge amount of overlap. Leveling everything lets you actually make everything yourself rather than having to buy all the mats that come from the other classes.