I don't consider this minor at all for myself, it is my BIGGEST complaint about subclasses in general in 5E, but Wizard is especially lacking.
Which is why when War Magic came out, I always used it. It generally helps in combat, and otherwise your PC is a "generalist" and not focused on any school of magic.
I think the big problem is that they used the School of Magic as a theme for the subclass, but the schools of magic aren’t REALLY school, are they? Is there really a ‘School of Abjuration’ as a physical building? It’s just some lame classification system that falls apart if you spend too much time thinking about it. This theming not only sucks, it shot out any interesting subclass right now. What even is ‘War Magic’?! It would have been better to base them on the Wizard’s relationship with Magic. Here’s what I would have done for the PHB:
The Academic: The Academic sees Magic as a mystery to study. They specialize in 1 (or more at later level!) school in particular, getting the cheaper copying ability, but they can learn freely from other School. A basic subclass that gets more spells, more rituals and can add more for cheaper. In this scenario, the base class learns less spells during level up, but the Subclass picks up the slack in providing extra spells. The Academic gets a bonus spell of their specialty whenever their base class gives them a new spell.
The War Mage: The War Mage sees Magic as a weapon to wield in battle. Inspired by the 4e Wizard, they develop ‘fighting styles’ that lets them wield the different implements in different ways to gain advantages. They can make effects last longer with orbs, they can make attack rolls more accurate with wands, and they can make use of close-range magic in battle by using their Staff as a defensive weapon. They learn less spells than the Academic but they get class features to set them apart. They get Light Armor proficiency to make them more battle ready and usually specialize in more direct offense.
The Lore Hunter: The Lore Hunter see Magic as a treasure to be uncovered. Somewhere between an Indiana Jones type adventurer and a Gentleman thief, this Wizard has the skills to make it through an old temple full of traps, or maybe to sneak into an Aristocrat’s library. Whereas the Arcane Trickster Is a rogue with a dash of Wizard, the Lore Hunter is a Wizard with a dash of Rogue, getting more skills instead of bonus spells. While they don’t get a rebate to scribing cost, they are much faster than other, allowing them to copy spells and possibly return the stolen book in a single night if they want.
The Diviner can stay but be renamed The Oracle or The Seer or something.