So you want scholarly (finding spells) and a boost.
How about some fun mechanics instead of a rework?
1. Prepared casters. They can prepare (int bonus) plus 1/2 class level (rounded doen) spells. All but 1 spell of a given level must be from restricted schools.
2. Arcane Tricksters can use a scroll as a material component. When they do so, the slot used counts as 1 level higher, and they can cast the spell even if they don't have it prepared or on their list. Doing this has a 50% chance of destroying the scroll. If the spell is not a spell on the wizard list, or higher level than the AT has slots, the AT must make an int(arcana) check against DC 10+5* spell level. On a failure they AT does not consume the slot or the scroll, and can try again.
3. EK can pick a number of signature spells equal to their intelligence bonus. Slots used to cast these spells count as 1 level higher.
4. Wizards can cast any spell directly from their spellbook. This takes 3x as long (and hence requires concentration), but attacks from the spell have advantage, saving throws have disadvantage, the spell counts as if it was cast 1 level higher, and any damage dice are doubled.