The problem I can see, and it's not really a problem actually, with those who want the schools noted (and I agree! They should be!), is that most spells are applicable to multiple schools.
In the case of WotC, I suspect it was the daunting task of making the choice for the player, if they were going to list only 1 school...which history suggests they would want to do. Keeping it open/leaving for the player/DM to decide is more "open" design. Fluff to taste.
Take, say, Shield. "It's an evocation!" many yell as a kneejerk because it is one of those "generic magical energy/force" spells. It is, most certainly, abjuration also as it is specifically a defensive/protection spell. But could it also be a conjuration? You are bringing this energy shield into being out of nothing...conjuring it up...Necromancy? You create a shield-like field of necrotic energy or shadow-stuff (same dimensions, same everything) that blocks incoming missiles/protects you.
Secure Shelter? Same story (though I'd be more inclined to make conjuration and abjuration the base and evocation the alternate possibility).
Is Prismatic Spray an evocation -just harnessed energy/-ies mashed together by the spell? A transmutation -many of the beams change things from one to another or teleport/maze you? A conjuration -bringing all of these many effects into existence at once? Are you conjuring a sliver or opening a rift to the Plane of Magic Rainbows? Or even a necromancy spell (are heavy damage and insta-death different beams anymore?)?? Or [I would think it's a stretch, but...] is it the uber-powerful version of the illusionist's staple, Color Spray...making it an illusion spell at its base (and conjuration to infuse with that lil' extra oomph of "reality" high-level illusion spells typically get)? What does it get labelled as?
Fluff can be written to explain (maybe not fully or entirely logical, but it is magic after all) pretty much anything.
Now, I don't get why WotC couldn't have just listed more than one school as was done once upon a time. But I suspect that that desire not to pinpoint...and to create a demand for their handy-dandy spell-by-class card packs...are the main reasons you don't see a "school" line in the spell descriptions.
For things that would be applicable to more than, say, 3 schools (and there really aren't many) just making it a "universal" tag, allowable by any school, would suffice...for me.