1) Simplicity and clarity of mechanics. The player shouldn't have to pore over descriptions or figure out "what on earth they were thinking."
2) Usability without a magic school.
3) Sufficient utility so that there is a reason to level up a school. So that when faced with a choice between Water and Earth/Air upon leveling up, the player doesn't automatically pick the second one but actually thinks about it. Or at least doesn't choose their father based on "who leveled Earth."
4) Not being OP at expert level; one must-have (Earth) is enough, no need to create more.
5) Do not make strengthened or weakened copies of existing controls. The spheres of application for spells may overlap, but they should not be entirely contained within one another. That is, if we make a weakened TP, it must have an advantage over TP in some (even if infrequent) situations. And conversely, TP must still make sense even when alternatives exist.
6) Whenever possible, create spells that require game skill to use effectively. In other words, it's better to make a fire wall than a lightning bolt.
Those were the gameplay requirements. There is also the requirement of atmospheric consistency—the spell should not be off-putting, should not feel like a "crutch" made for online play, and should have ideological continuity with existing gameplay mechanics. That is, when looking at a spell, you should ask yourself: "Could NWC have made such a spell?" Or "Could a similar spell have appeared in Heroes 2?" (where there were no magic schools).
I understand that for online players, any mechanic that improves balance is acceptable. You could forbid upgrading gorgons on Jeba, you could allow joining levels 1-4 at the start for Inferno, you could allow building a library with 211 in computer-controlled Towers, etc. But since HotA is being made for the widest possible circle of players, and the offline community is significantly larger than the online one, the requirements for gameplay harmony are much higher.