However, I'm starting to feel that from a narrative and balance, the warlock - specifically the tome warlock - is a better depiction of a generic "fantasy mage" (which is not the same as a D&D wizard!).
I came to this realization watching the Dungeon Dudes 's game on youtube. In their current campaign, their party mage is a warlock (GOO, tome). This warlock is from a family of wizards, he joined the academy etc and... sucked. He just didn't have the talent, at all. So his parents made some arrangements for him to find a certain ancient text and ... voila, he's now a "mage!". (this is background stuff, not in the actual campaign).
Because of this, the character is really trying his hardest to "be a wizard", but his toolset is limited. Only a few slots available at any given time. A lot of "shenanigans" to compensate. BUT he's still an effective mage, which some really clutch moments.
And I realized, watching him, that apart from the numerous reference to his patron (Bruce, who looks like a cat), a Tome Warlock is much more like a generic fantasy wizard, or how a wizard is in several other games. They can't fix every problem with a spell (because they don't know that many), the tome aspect makes them "bookish" a bit, they have to rely on wits, guile and luck to fix other problems etc... not at all like the swiss army knife, spell for any situation wizard. This makes them more balanced too! The only change you might need is changing the main stat from cha to int and perhaps tweak the skill selection a bit...
Am I on to something? does this make any sense?