The idea of getting them from trainers and combining them is cool, but I think the perks should not be passive bonuses like -5% spell cost or +10% fire damage, I would much rather prefer perks that add something new to gameplay, and are more visible than passive bonuses. Like instead of what you said, perks for destruction would give secondary effects to spells, like what I said before about a DoT effect, a slow effect, or a paralysis effect. or Mastery in spear skill lets you throw your spear as a very powerful attack. passive bonuses like +10% fire spell damage would be boring, and not very noticeable.
Many of them would be, such as the extra spell effects or special attacks that I mentioned. They would just both be among your options, and up to the player to choose on what they want.