The 5e spells themselves need a revamp. 5e did a great job of removing broken spells. But there are MANY subpar spells that are strictly inferior to other spells in the same spell level.
Force Cage might be the only broken spell in 5e. In any case, it merits a rewrite to keep the unfun experiences of Fighter players in mind. The spell pretty much removes these players from gameplay, in a way that is unpleasant and nonentertaining.
Wall of Force is balanced, but it is strictly superior to the other wall spells. Probably, the other wall spells need to demote to a lower spell level where they become more competitive against the spells in the lower level. Alternatively, the wall spells get a rewrite to become more powerful so as to be more competitive versus the spells at their current level.
Fireball probably needs to reduce its damage output to be more comparable to other spell level 3 spells. It is ok if the Wizard has a class feature that augment it. Compare how the Warlock has class features to augment Eldritch Blast.
Reverse Gravity becomes available in a tier where flight by various means is normal.
In a combat encounter, "dead" is the most powerful status condition. Only the martial classes inflict this condition well.
A decent wizard will enable the party to inflict dead status with far fewer resources expended than without that wizard, for example by allowing the party to engage the enemies in serial rather than in parallel.
In one instance at my table, a high level wizard decided to turn against the rest of the party (a fighter, rogue, druid, and warlock). Granted, he had the element of surprise, but this really ticked me off, so while I was endeavoring to run the encounter in a neutral manner, my rulings were almost certainly biased in favor of the party. The wizard nevertheless very nearly TPK'd the entire party. They only survived because they used two wishes (from a Ring of Wishes) and retreated into a Staff of Sanctuary, after 3 or 4 rounds of trying to take the wizard down.
Now, I'll grant you that PVP is a very poor metric by which to be comparing classes in D&D. That said, can you imagine any scenario whereby a fighter could do the same? I can't. Again, this is not to say that classes should be balanced around PVP. But they ought to be equivalent in effectiveness within the game. I've never seen a scenario where a fighter even comes close to being able to take down an entire party. At best, the fighter might manage to kill one or two, but four? Not a chance. And this illustrates the power disparity between the two. Which doesn't even get into a comparison of utility, where the gap is exponentially greater.
Can a fighter and wizard both contribute meaningfully at the same table? Absolutely. Particularly if the wizard player is willing to share the spotlight.
Are wizards all that? Most definitely. A wizard who doesn't want to share the spotlight can hog it with far greater effectiveness than most other classes can.
Is that fundamentally a player problem? Yes. However, the classes should nonetheless be balanced such that if you have a problem player, one class doesn't pose an exponentially larger problem at the table than another. If not, it clearly demonstrates an issue of class balance.