The 8 spell schools are very D&D so they have to go in the Remaster. For specialist wizards, they'll instead have actual schools that they studied at, with various themes like the "School of Battle Magic", with a predefined list of spells they specialise in.
Spell schools were invented for Dragonlance in the lead up to the 2e era. The idea of an Illusionist is probably demonstrable enough outside of D&D, but the rest are pure TSR lore.
Other fantasy worlds slice up magic differently. I personally would like to see the concept of magic schools stick around in some form but the D&D schools always felt a bit arbitrary in their divisions.
Enchantment also feels like it could stay, though maybe with a different name; although realistically it's already kinda covered by the [Mental] trait. Anything that previously referred to "enchantment spells" could be changed to refer to "mental spells"
Abjuration, Conjuration, Transmutation, and Evocation were always the ones that felt the weakest in terms of having well-defined boundaries.
I agree that the schools always felt a little arbitrary. Abjuration in particular always felt kinda weak to me, even in concept.
I think they could probably just leave it to a potentially open-ended set of traits. Some could even have multiple, which helps with the arbitrariness. Characters could specialize in spells that have particular traits.