A few ideas to improve the WHM from a SCH player
I'll start by saying that the differences between the classes are starting to be more apparent, and that after playing with a WHM partner following 2.1, I feel there need to be more improvements to WHM play that bring them back in line with how versatile and efficient scholars are.
Versatility
White mages struggle to keep up with scholars in terms of actions per minute. This is due to the scholar's advantage in simultaneous control of self and fairy (improved in 2.1, which I am pleased about!), which is even better with the addition of proper manual fairy AI options and mouse-over macros. These changes allow me as a scholar to target a player or monster for personal casting while also commanding the fairy to heal a separate target. Doing so does not require separate targeting selections. In order for a WHM to remain competitive in versatility, I would suggest making Regen into a free spell off of the normal spell GCD. The justification is to allow WHM to improve their actions per minute while also having comparable secondary healing output as a fairy for the same mana cost as fairy heals, while still retaining the "WHM-ness" of the function. This leads me to the next topic:
Efficiency
It's no secret that every class in the game is reasonably efficient with the exception of white mages. White mage mana is a liability. Ask your bards how often they play Mage's Ballad compared to how often they play Army's Paean. Consider the changes in 2.1 which move white mage play in the direction of Cure III as a response to high-stress AOE healing and away from reliance on Medica II for those purposes. One thing that these changes did not help with was improving the mana liability of the class. Arguably, things are now even less mana efficient. Consequently, I have a few suggestions to improve efficiency:
1: Free Regen
By having a free, off-GCD Regen, white mages can solve minor healing concerns (e.g., your monk stood in an AOE) with similar outcomes as scholar fairy use, using a free, low-potency solution that does not detract from your primary healing duties.
2: (Critical?) Regen ticks reduce the cooldown of Shroud of Saints by X seconds
By providing an intra-class synergy with a core class mechanic, it will be possible to encourage skillful use of Regen in order to gain quicker access to the WHM threat and mana relief option. The conditions by which access to SoS is improved may depend on the itemization that developers want white mages to aim for. For example, if spell speed is desired, have spell speed increase the rate of Regen ticks. If crit is desired, have critical ticks reduce the SoS cooldown even more, etc.
3: Streamline Medica II
Remove the front-end heal and reduce the mana cost proportionately. Now the spell is the intended background heal but better optimized for that role.