Yeah, the inconsistencies of the schools causes future mechanics that depend on them to convolute as well.
It seems to me the most effective way to organize spells is thematically. When players create character concepts and DMs create worlds, themes are the most salient consideration.
Many mage concepts do well to focus on two themes simultaneously, such as making cantrips and the highest spells available cohere to these two themes.
Re healing. Having organized every official spell for my own use, I find it most useful to treat healing as its own spell theme.
The "purpose" of healing is Abjuration, being part of protective defensive magic, generally. Abjuration is a decent keyword tag, even when organizing by theme.
The purposes look something like the following:
Offense / Defense
Mobility / Barrier
Detection / Stealth
And I consider summoning allies, pets, companions a seventh spell purpose.
But themes are something different. A spell of a specific theme might fulfill any of the above purposes.
There are different methods of healing: positive energy, shapeshifting, and morale. Each of these is a different theme: planar, body, and mind. While I treat the life energy of healing as its own theme, it pairs well with any of these three.
I see necromancy as a theme that focuses on death and undeath. I dont see it as relating to life (healing) per se. That said, a mage that focused on both life and death for the two main themes, could choose healing and necromancy for the central concepts.