A great deal of truth in that. However, Wizards are also "solution man" - or should be. While I've never met a wizard player (and character) that didn't enjoy their evocation spells ("Spell go BOOM!"), where they really shine (or should) is in their ability to solve problems ("Hold on. I've got a spell for that."). That does require wide-open access to spells, though, which is something a lot of games have trouble providing.
And unhappily with 5e's prohibition against buffs, one of the more useful problem-solving tools for the Wizard was taken away. Frankly a classic wizard complaint would be something like: "Years studying the hidden mysteries, plunging into the arcane depths of history and theory. Mastering the subtle art and science that is magic. Wrestling with the actual rules of reality - and winning! And what do you, my fellow party members, only ever want me to do? Blow up the monsters! ARGH!" {Later, in private: "Hehehe, monster go boom.")