This suggestion is for a new damage type to be introduced into the game: Heal Damage. Weapon and Spell damage only effect offensive effects. In addition, hybridization should be done with and revert to Max stats making a difference again. Max HLTH is used to determine the effect of some skills, so too should max magicka and stamina.

In addition, Max Magicka and Stamina should be THE main modifier for damage; with Weapon, Spell, and Healing damage as buffs to the main stat (again, main dmg stat being determined by max mag/stam)
Healing damage would be more effective the LESS Health one has! These changes would create a real dynamic between classes, class skills, dmg and healing, etc.

Stamina: Increased value increases overall Weapon Damage
Magicka: Increased value increases overall Spell Damage
Health: Decreased value increases overall Healing Damage

Wpn/Spell Damage buffs could increase all damage types (as they do now) if it was a buff rather than the main method of increasing damage.

Stacking Health helps you live longer, but it is done at the expense of Weapon/Spell/Healing
Health regen should be constant and not effected by silencing, debuffs, etc. It is a form of constitution, etc.
Health regen might actually matter if players had to actually strategize staying alive vs. self heal off their max offensive Dmg etc.

Since Stam/Weapon players are not 'mages' and should not be able to 'cast' a heal (besides pots). All Stam healing abilities could funnel through health regen (like Vigor, 2h heal, DW heals, etc; and where magicka ability healing provides real direct heals, buffs, dots, etc.
Potions and frequency of potion use would also become an important survival dynamic.