Pedantic
Legend
So you're saying the game has no mechanical or setting level thematic constraints on what wizards are like and mechanical incentives to use specific spells? In that scenario, one wonders what claim to thematic appropriateness the "classic" wizard archetype you're suggesting has. If you want wizards to use Fire, then limit their access to other abilities and/or make Fire a strongly incentivized choice. If you don't want to do either of those things, then I'm not seeing a dilemma in the first place.
What is the good the player is supposed to be serving by making these choices? The structure of this question implied this was something other than "do you always pick the most mechanically effective option." If the designer wants variety in Wizard choices, they need to present multiple effective options with incomparable or situational effectiveness. If the design wants a thematic core of Wizard abilities, they need to design the class thus to either exclusively or preferentially present those abilities. If the GM wants to use an existing design to those ends, they're taking on design work, even if that design work is as straightforward as prescribing a specific set of spells for Wizards to use.
If those aren't concerns, then this isn't a problem.
What is the good the player is supposed to be serving by making these choices? The structure of this question implied this was something other than "do you always pick the most mechanically effective option." If the designer wants variety in Wizard choices, they need to present multiple effective options with incomparable or situational effectiveness. If the design wants a thematic core of Wizard abilities, they need to design the class thus to either exclusively or preferentially present those abilities. If the GM wants to use an existing design to those ends, they're taking on design work, even if that design work is as straightforward as prescribing a specific set of spells for Wizards to use.
If those aren't concerns, then this isn't a problem.