If Detect Magic and Read Magic cantrips were Divinations instead of Universal, we would see much less specialist with Divination banned.
I don't think this change to banned school is an improvement except that it's simpler, but it not a bad change either. As a matter of fact, it doesn't change that much but makes Necromancers and Diviners a little worse.
I never liked the specialization rules in ANY edition of D&D, specifically I think they have great flavor (so much that this is the only class feature that has even generated different character names, "Necromancer", "Evoker" and so on) but the banned schools mechanic never made any sense. The explanation that a specialist must dedicate more time to his favored school so doesn't have any time for all other schools seems fine but it is not: there is nothing else in D&D which a character is FORBIDDEN to learn unless it is either a specific feature of another class (and you learn it by multiclassing) or either there is an ethical reason to prevent it (alignment, oath, religion). Everything else is available, except banned schools to a Wizard. A Wizard who is supposed to be a master of knowledge, why should he be forbidden to learn one single spell from a school?
I have always used the rules as they are, and they work fine after all, but I never got to convince my players why it works this way.
I think that if there was no banned school at all, the Wizard would still be a very balanced class. Of course it means no generalist Wizards anymore, but who cares? There aren't Clerics without domains or Rangers without favored enemies and nobody complains about that.