I could never understand the other things, but I still think that Temper and Enspells at least made some sense why they were not able to be cast on others or made AoE, since they are exclusively for boosting the melee capability of the Red Mage.

You can say that Red Mage is a bad melee all you want and maybe you'd even be right, but they are what SE tried to give to Red Mage for its melee side, and not for enhancing others.

On the rest, I'll say it again. Gain-STAT? WHM can, so whynot RDM? Refresh II? BRD can, why not RDM? Haste? WHM and RDM should be able to with a unique spell, and Haste itself should be Accessionable.