Its actually quite simple from a job design standpoint why things are the way they are in regards to mana. Scholars have to micro manage their pet in order to be able to heal effectively so having them manage mana in a meaningful way would really up the difficultly of playing the class, which is already more difficult than not.

On the other hand White Mages are much more straight forward but needed to have a system like the scholars pet that they could manage. So it was decided that White Mages would have to utilize the varying heals they have effectively to manage their mana usage. In order to not make that system not completely brutal shroud was created as a safety net. If the White Mage is using the wrong heals and running out of mana it is also likely they have additional threat from overhealing so shroud is your "I screwed up" button. As mana pools continue to rise the need for shroud will lessen since you will naturally regen more mana and have more mana to spend while the cost of your heals stay the same.

It's easy to look at Scholar and the fact that they don't have to worry about mana very much at all and be envious but White Mages don't have a pet that makes up a large portion of their healing to keep from dying, and micro manage because the AI isn't all that great.