Even in theory, it's much more fiddly than it needs to be. Have you tried actually building a character with it? It's a real pain to go down the list of Arcane spells cross-checking each one's school to be sure it's kosher for bards. If they do actually stick with this system, I'm quite sure they will "multiply it out" to generate spell lists by class.
I wouldn't mind an overhaul of the spell classification system, but the first step toward such an overhaul should be to junk the traditional eight schools. The problem with the schools is that they're defined as "spells that do X," which means they assume every spell in D&D does exactly one of those eight things. And that just ain't so. Look at healing magic. It was necromancy in AD&D, conjuration in 3E, evocation in 5E, and now apparently it's going to be abjuration? It's patently obvious that it doesn't belong in any of the eight, but every spell has to go somewhere, so it gets jammed in wherever the designer of the moment thinks it fits.
It's fine to preserve the traditional eight as wizard specialties, but the spells themselves should be categorized in an open-ended way which can accommodate the immense variety of spell effects in D&D.