I divided magics in my homebrew world/system into 4 (base) categories. It works pretty well.
Mine are not as broadly titled/spanning as teh PF2 categories. It seems these would be significantly more useful and easily combined for various classes.
"Material & Vital," for instance, seems like they would probably give you a decent Necromancer. "Spiritual & Material" could give you a workable Shaman or potentially some flavor of Witch. etc...
My own adheres more to D&D traditions and are simply carved up into: Divine, Nature/Natural, Arcane, and Illusion [which is still/a subset of Arcane magic).
So you can easily see how things work out:
Cleric = Divine - protections, divinations, healings, some (both material and spiritual) travel/movement, some effecting/changing the material world.
Druid = Nature - anything to do with plants, animals, the weather & cardinal elements, some protections, some divinations, some healing, some spiritual/otherworldly connections (traveling to, conjuring from, etc...)
Mage["wizard"] = Arcane - all the usual suspects, effecting/altering the existing material world, effecting/altering the mind, generating/controlling/and/or undoing energies, some travel/movement
Illusionist = Illusion - effecting/altering the mind and perceptions, light/color/shadow/darkness generation/control/undoing, some energy generation/control, some conjurations. Roughly 1/2 the spell list can be found on [full] Arcane list and the other 1/2 are specific to the archetype.
Paladin = limited Divine
Ranger = limited Nature
Bard = limited choose between Nature & Illusion
Witch =choose between Nature & Illusion (class features allow limited spell selection from other lists)
This, of course, ignores (in the "Base" of my homebrew game) other specialist wizards. Given the precedent set by "Illusion[arcane]" magic, Necromancers would need a "Necromancy" spell list consisting of roughly 1/2 things from the Arcane list and 1/2 specific necromantic-themed /necrotic spell effects, Conjurers would need a "Conjuration" spell list, et al.
So it does make things a bit "neater" to be able to categorize things in distinct segments. Perhaps a bit more symmetrical (at first), easier (I feel) for players to wrap their heads around..."What spells am I choosing?"<looks at pages and pages and pages of lists and alphabetized spell descriptions in dismay>"This list here. These are the spells you can choose."
I mean, Pathfinder being Pathfinder, I fully expect that if they begin the new edition with these 4, you'll have 20 magic categories by the end of the following year and be right back, essentially, to where you've started. That being the case, I would advocate to just keep the individual class lists they use now. Draw from whatever "Type" of magic you need, if there's a spell that's thematic to the class/archetype, then just put it on the class list.