Yes, it does. Or at least, it means that the mechanics must reflect some degree of that complexity. Otherwise the lore feels like a lie in play.
The idea of having an eldritch blast spammer with lore that you are enacting spells based on complex understanding of spellcraft through long study is just laughable. It would be like saying your greatsword barbarian is an archer.
Besides, a 5e Wizard isn't exactly learning the formulas that make spells work.
They cannot be entirely independent. Only classes whose class fantasy can reasonably be simple should have simple class mechanics. If you want a simple arcane spellcaster, there must be at least two arcane spellcasters.