Having a literal book for casting in D&D doesn't make sense at all even for a wizard. A wizard casts by memory - that's the whole thing about preparing spells.
Preparing a new list of Wizard Spells requires time spent studying your Spellbook and memorizing the incantations and gestures you must make to cast the spell...
Wizards can’t not have a spellbook in 5E… it’s core to their class. Although, it could be reskinned into something else like a crystal, tablet, whatever. It’s part of the balancing of being able to have access to so many spells and it serves as a record of what spells you’ve learned. Also, it can become a plot device if it’s lost/stolen, or if you find a spellbook from another wizard.
And preparing spells is literally reading it from your spellbook into memory. The number of spells you can memorise is limited. If you don’t have a spellbook you can’t change your selection of memorised spells.
