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If a wizard chooses to specialize in a school, they gain benefits at certain levels, in exchange for only being able to cast wizard spells from that school, and having less spell slots. So, a generalist wizard has more latitude in spell casting more spells per day, which makes up for not having special benefits. On a side note, I think all wizards should get an extra meta-magic feat whenever they take a level in wizard when they would gain a feat, and wizards should be able to substitute their intelligence modifier for their DEX and CON modifiers for AC and HP, respectively.

• Evocation: Evokers (Which could be also called warmages, due to most evocation spells being focused on dealing damage) have 1 favored spell per level of wizard spells they can cast (1 favored spell when they can cast 1st level wizard spells, another when they can cast 2nd level wizard spells, etc.). When an evoker uses a favored spell, they have a 50% chance (on a d%) of managing to gather enough residual elemental energy from the spell to treat it as not being expended. This chance decreases by 10% each time the spell is used between long rests.
• Necromancy: Necromancers gain feats from the Necromancer specialty as bonus feats when they reach certain levels of wizard (1, 3, 6, 9, etc.) along with other special benefits, like having your undead servant get stronger as you gain levels in wizard, having multiple undead servants at higher levels, being able to burn hit dice equal to a spell's level to regain the use of that spell, etc. (IMO, Necromancer and Magic-User feats should stay feats, as not only wizards would benefit from them)
• Illusion: Illusionists' school benefits allow for stronger illusions, higher save DCs against illusions, extra illusion spells, and maybe illusory effects gaining special benefits that make them seem more real.