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Think about PF2's spell heightening rules - a Sorcerer needs to learn a spell at each of the levels they want to be able to cast it at (with the Spontaneous Heightening feature helping minimize the actual need to do so since it can cover your favorites), but a character may not have enough spontaneous heightening uses to cover all the things they want to do. Prepared casters like Wizards have to prepare spells at specific levels in order to be able to cast them at that level, so you could prepare 3rd and 5th level fireballs at the same time.
In a spellbook, while there's not much use for it, you're technically allowed to write multiple copies of the same thing (it's more useful when you get multiple spellbooks, and may want to create a backup to keep at home or something like that).
So we have improvements to make in terms of how to present things, and we'll need to do more to flag the duplicates, but I'm not sure we can actually remove spells from the list when added to your character without messing up some of the heightening options.
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