I like to think of this game to be similar to Dominion. Every match has a unique set of spells, of which the game is to figure out how to optimize and learn the best combination of them, in order to get the highest score before the game ends. If the game would be about who can learn all 7 spells faster and/or at a higher spell level, the game would be a lot less fun. Then it's just a color matching game.
I love this analogy and probably would've actually quit the game already if not for this. Allow me to suggest another one that may be better. Think of it as a game clock. The familiar board even looks like one, sort of. It's similar to games like Azul, in which that game will inevitably last 5 rounds unless all players slow roll. Except this "game clock" is better, since it also works as a mechanic to help filter your token pool, making your game overall more consistent. Additionally there are ways to interact with or manipulate the "clock", using many of spells that the game is based around.
Your "penalty" though is too harsh imo, but that may just be a personal opinion. There are niche situations where it's better to not store, if you get a high value spell 1 turn earlier or if your pool is full and not storing will enable you to get a high scoring spell. The comparison would be playing starvation strat in Stone Age.