So here's an idea. What if after a certain point (say, level 7) Fighters progressed two (or even three) levels of abilities for every one that full casters progressed? So my level 8 wizard adventures with a level 10 fighter. My level 10 wizard adventures with a level 14 (or even 16) fighter.
Is there a point there where the maths work out such that being a basic linear fighter matches up to being a quadratic wizard?
Probably not, no. The reason I say this is the Fighter's problem isn't their combat prowess exactly; more levels would just upset encounter balance as they become that much better at dealing damage with increased durability.
What the Fighter lacks really comes down to narrative power and a broader toolbox. A Wizard's spells present potential opportunities- dramatic momentum shifts in battle, dealing with large numbers of foes quickly, and tackling challenges in a more outside the box fashion.
A Fighter can be counted on to, well, fight, and deal excellent damage to one foe at a time, as well as to be tough to take down, and they are fairly consistent at doing so. A Wizard might struggle in an adventure, or they could turn it (and possibly even the campaign) inside out.
A scenario I like to use to demonstrate this goes like this:
The players are tasked with defending a small town. They have five days before a large force of enemies arrives to stomp it flat.
The Fighter might try to come up with a plan to defend the town, form a credible militia, or create defensive structures. Their means of doing so is basically ability checks, with DC's and time required set by the DM.
The Wizard could do this, or-
They could create weapons and armor for the townsfolk with Fabricate in ten minutes. Use an invisible familiar to gather intelligence on the enemy force. Create fortifications in a short period of time with Wall of Stone or Move Earth. Make a building difficult to assail with Guards and Wards. Call for reinforcements with Sending far faster than any rider or messenger bird.
Maybe the Wizard can't do any of these things, of course, but the potential is certainly present in their spell list (it could be even worse with Clerics and Druids, as while their list isn't as deep, they can petition their deity for any spell on their list after a long rest, no matter how niche or obscure!).
Or say your campaign has lots of downtime. The Fighter might forge a new suit of armor, make some contacts, learn how to use a new tool or learn a new language, or just go looking for a battle arena to make some coin.
A Wizard could break the economy by using Fabricate to turn raw materials into trade goods. Mentally influence a powerful NPC. The narrative power granted spells is extreme, and the game isn't balanced around this in any way shape or form- it's completely up to the DM to figure out how casters don't dominate their world (usually with deus ex machina or other casters).
The balance point of spells is the need to ration them out over the course of an adventuring day. But if you're not currently adventuring, or a given day has less encounters, there's more opportunity for spells to get out of hand.
A savvy caster can warp the game around their activities in a way you wouldn't expect from a Fighter, Barbarian, or Monk. And the DM has to do extra work to mitigate the impact on their games.
Now you could try to rebalance what magic can do, and reign it in, but as far as D&D the game goes, spells as they currently exist aren't going anywhere- the majority of consumers apparently like the magic system the way it is, thank you very much.
What I always find strange is that the majority of consumers also seem to like their martials exactly the way they are as well- good at fighting and doing things you'd expect Fighters and Rogues to do. They apparently don't want abilities on par with casters and don't see a problem with their hypothetical potential, because well, it's just that. Hypothetical. It won't show up in every session, every adventure, or even every campaign, so what's the point of worrying about it?