So in other words.. White Mage Unlocked + Monk Unlocked = White Monk Quest Available.
Each job should actually have lore that explains why they are not exactly guilds, but more like they are forms of battle that were taught and used by the Grand Companies during times of war. Jobs are advanced war techniques that allow one to focus and become more efficient in large groups.
The confusing thing is this: You are putting Jobs first before you are considering the Class/Weapon you are using.
This is a simple way to understand that Jobs will not replace Class.
You are using a hand-to-hand weapon. You are a Pugilist.
Since you are a Pugilist, you can select the Role as a Monk.
You are now a Pugilist, performing as a Monk.
Being a Monk isn't more important than the weapon you use. In fact, its the weapon you use that is important to your role as a Monk.
You equip a Battle Staff. You are a Stavesman.
You want to perform the Role as a Monk.
You are now a Stavesman, performing as a Monk.
That is pretty much how it would work if multiple classes were able to perform as Monk.