That's not a solution that's another option with it's own tradeoffs. The most obvious being not having any magic at all to represent years of magical training. If it was Old School Essentials then I would do that, but WOTC D&D games have complex mechanical character defining options.
Depends what you mean by overhead? I thought we were talking about time spent looking at character sheets. 4E has a lot more stuff to track and keep track of, but playing a Wizard in 4E would mean I would spend a lot less time looking at my character sheet than I would spending looking in my book, or google, or at spell cards in 5e. The powers are shorter, they're less ambiguous, they can be read almost at a glance; the effect is clear.
And there's an order of magnitude more time spent discussing spell effects with the GM and what they can achieve than in 5e. (Which is not necessarily to the benefit of 4e, as a lot of the stuff discussed involves the limits of more creative spells such as illusions).
Basically, I find it hard to believe that players spend more time interacting with the world and less time looking things up in a game where almost every single character has a long list of spells. If we were talking about Barbarians of Lemuria, I would grant the distinction.
