Spell Schools as Skills

Maybe it's an auxiliary skill, so an Enchanter could artifice a ring of enchanting, while an Ice Wizard artifices a wand of ice shot.

Correct - because INT doesn't boost magic in this, only your skill, a high INT mage has more mana, but a warrior could pick up a spell school (healing for paladins, ice magic for death knights, etc) just not get as much use out of it. So a warrior could chuck 1 powerful spell or lots of weaker ones.

I tend to avoid actual item crafting as a skill, if someone wishes to make a flaming sword I normally say to send them on a quest to get the bits. Otherwise we'd see flaming butter knives and a real toast industry.

mostly my complaint is the semantics.

I FUCKING HATE when people use the word "enchant" for "magical compulsion"

enchanting AND high skill in the category you want to enchant the thing with.

But it's not always compulsion, sometimes its suggestions or nightmares or simply making people forget something.

There is literally nothing wrong with using enchant to describe placing someone under a magical compulsion you autist.
Also

I'm with you there on the word choice. It's a little sad that we can't use Enchanter to mean "one who magically captivates" but it's become to mean "one who bestows magical effects to items" so much that it becomes awkward to use any other definition.

High magic fantasy, but few magical items? I can dig it.

The real issue I'm having is making clerics, priests and paladins separate.
Plus bard things. But I don't think they deserve their own spell school.

Why are you going with classes at all?

Because if someone wants to build their skills in such a way to mimic the standard idea of that class, then people don't have the option to do so.

How about priests and holy warriors have access to whatever schools fit their deity, with holy warriors limited to 2-3 schools max? Your standard priest/holy warrior would take Abjuration & Healing, Conjuration & Scrying, and an appropriate elemental school, but other possibilities exist.

Bards would take Conjuration & Scrying, Motion & Levitation, and Necromancy & Enchantment (both because mind control spells are very Bard and the school lets them sing to the bones or play a song so well even the dead cannot resist joining in).

A lot of this terminology is all open ended, so I'll throw in something I don't think you've touched on yet.

Have a single work be achievable in multiple ways. Take 3.5's mage armor: fuck abjuration. You're an illusionist? Mage armor is a shifting cloak that obscures your position or ornate looking plate that isn't real but will stop a blade of you think it can. You're a transmuter? Mage Armor is what you call it when you harden your skin or clothes. Diviner? Precognition and fast reflexes. Necromancer? Fuck it, you tank that shit and stitch your flesh back together with magic.

Which is not to say don't have your skills. I love the idea and am trying to do something similar. But necromancy is divination by way of talking to dead folks, as opposed to regular old divination--the words we're encouraged to use have a lot of semantic baggage.

TLDR use skills but give them different themes

I would probably assess the in-world mechanism behind the magic, then just classify spells by different manipulations of that mechanic. For example, I run a homebrew system where the source of magic is breath, which can be augmented in various ways to create exaltation similar to the voice of god, which therefore have power. The subclasses are abilities which require you to hold breath within yourself to form a stable change in reality around you, violent releases and proclamations, and inhalations meant to capture and temporarily suppress an aspect of reality. Each of those things functions in utterly different ways, hence they are schools.

So.. get all the spells you want in your game and add skill prerequisites perhaps?
Getting your Mage Armor effect requires you to be a Novice Illusion skill, an Excellent Divination skill level or a Good Necromancy skill level.
Different spell effects are 'unlocked' at different levels of skill. Some are unique to a School whereas others can be replicated by most Schools in some form or another.

Dabbling in many schools gives you an incredibly versatile toolbox and can cast many effects using the easiest method/lowest skill requirement but forbids you from the advanced spells which demand you to sink points into their sole affiliated School. No amount of Fire magic is going to create a zombie thrall for instance. You must be a full Necromancer.

I think that these ideas are good, but rather the prescribing a difficulty for each school, I think it would be simpler to benchmark things into a difficulty range based on the school's own terms. That saves you from having to be more creative than every player that will ever play your game, and enforces interesting utilities of different types of magic you wouldnt have seen coming.

To be fair, the system I'm trying to make rules for is alters and archetypes, so it's pretty fucking bare bones.
So I would run that like this--my best archetype is a fire wizard, and I want to cast mage armor. I'm going to roll for fiery protection and the degree of success will dictate how much harder it makes me to hit. Since fire is insubstantial, this will actually be pretty poor armor that burns my attacker.
Whatever spell effect I want to do, I run by the GM and we establish a difficulty for it. Maybe burn more mana to boost casting, and if I practice a spell a ton then maybe I add "signature spell: fire armor" to my inventory and it gives me a bonus to rolls