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In my house rules I gave spontaneous casters the equivalent of "Signature Spell" for free to all of their spells. Spontaneous casters/Sorcerers are supposed to have a limited Spell Repertoire, but be able to use them more often and more freely, so now they can. To balance this, I want to give something to Prepared casters too. Clerics and Druids already get access to pretty much all of their respective lists (the main restrictions being alignment, such as Good Clerics can use Heal while Evil ones can use Harm). But Wizards only get a portion of the Arcane list. By the book, they start with 10 cantrips and 5 level 1 spells. They add 2 more spells when they level up, and can find more in books and scrolls. In games I've played in, finding an enemy spellbook was a rare thing and usually only happened because it was in the module or because we needed a specific spell to continue.
So here is what I propose:
When a Wizard increases in level, they may add a number of new spells to their spellbook for free. They get either 2 or their Int. mod, whichever is higher. The spells must be from levels they can cast.
This will add some of the flavor of Intelligence adding to your spell lists, but it won't actually increase their power since they can only prepare a number of spells equal to their slots. This just gives them a few more choices (about double for most Wizards) in what to prepare, thus strengthening the Wizard's role of "lots of spells, but what to prepare?" to contrast with the Sorcerer's "this is my fixed repertoire, but I can use them a lot more and more flexibly".
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Given the other houserules you've introduced this looks good to me.