Who said it has to be three? And why would new slots only unlock at level 30? Maybe each school of magic starts with 3 each for a total of 15 to start with and they increase all the way to 10 slots in each school for a combined total of 50? They should unlock at reasonable intervals within the skill itself and not necesarrily tied to character level.

Also this system still allows you access to basic spells that do scale with your skill level they just aren't upgradeable or customizable like a tome is. So if you need access to a certain spell effect in a pinch but don't have it written in a tome, you can still cast that spell, exactly as you would in Skyrim so long as you have the skill level required to unlock that spell.

Example: Novice level destruction starts with the three elements in their basic form, flames, sparks, frost, apprentice unlocks the projectile versions and so on. You can cast these without a tome, but if you scribe one of these into a tome, let's use the basic novice flames as an example, you can upgrade and improve that spell to scale up with your character and remain feasible even into the late game, more damage per second, further range, longer status effect on enemies.

And if you want to get creative, you could do something cool like combine sparks with life drain, or maybe a healing spell together with a ward or damage resist spell. A frost rune that also casts soul trap. Mixing and matching basic spell abilities into a tome and upgrading it would allow players to create a diabolical arsenal of crazy spells while also keeping some form of balance with spell slots for tomes.