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All conjectured explanations aside - the bottom line why mages can only cast a limited number of spells per day is GAME BALANCE!!!
This goes all the way back to the very earliest days of PnP AD&D. Mages are very weak at low levels, but they are easily the most powerful class at higher levels. Limiting their spells is one way to limit their power (although it is still impressive). Having unlimited spells per day would make them demi-gods (or better) on the power scale.
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Cerek the Calmth
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