What do you mean by "choose"? Do mean casting or choosing the spell beforehand.
Sounds good, but i think the whole system eliminates the process of preparing and selecting the spells you will be able to cast. As i said already, let me choose (before the encounter) which low level spells are on cooldown. Using one casting pool for all mid level spells leads to another problem. You will most often only use the spells in the highest spell level because they will most likely be more powerfull.
To follow your system:
Level x Mage
[Low level spells]
Level 1 spells [zap, burning hands, push away*]
Level 2 spells [stun*, bark skin, play dead]
The spell with * can be cast with cooldown of maybe 30 seconds. The selection which has a * is restricted to certain momets, maybe resting. The other spells are cast normally ( or maybe with a higher coolown like 2 minutes). As you level up you slowy got more * to distribute.
[Mid level spell]
Level 3 spells [flame arrow, fireball, haste]
Level 4 spells [summon x, spell shield. power word dance]
You can maybe cast five level 3 spells before this spell level is locked for this combat (or maybe only a real long time like 10 minutes). For level 4 spells you can cast four spells.
Maybe with certain perks, feats, whatever you can also set some * for 1 or 2 spells. Then this spells only count as 0.5 spells and can be cast twice.
[High level spell]
Using the grimoires you select which spells are available. You can switch grimoires mid-combat but with a big drawback (cooldown, 2 spells less to cast, only half as powerfull).
Level 5 spells [flamestrike, mass haste, lighting ball]
Level 6 spells [meteor, flying sword named after a famous mage, power word suicide]
You can cast maybe two Level 5 spells or one Level 6 spell then this spell range (both spell levels) is locked down until you rest or for x hours.
In this way there is still some preparation possible for certain encounters because you have to choose which to cast more often instead of always having the same low level set of spells you can spam. Leads to a more individual set of spells for every mage.