Fighters do deal damage relaibly and if the game was solely focused on combat I think this would be true. When you consider all 3 pillars Fighters can't hold a candle to Wizards potential, or for that matter Rangers or Paladins.
The only way this is not true is if you severely restrict spells available to Wizards. If you keep them limited to 2 spells per level by not providing scrolls as loot or the ability to make or purchase scrolls then you can keep this statement true through all 3 pillars by limiting their available spell selections. Even in this case though, Clerics and Druids will still outrun fighters by quite a bit.
Sure as DM you are literally god in the game. You can use anything you want - have an entire adventure in a non-magic area, and that is without even houseruling anything.
Depends on builds and priorities.
If casters happen to have the right spell prepared and
if they have the spell slot available and
if the NPCs don't notice and take exception to the PC casting spells and
if the DM doesn't enforce the rules like Charm Person only makes the NPC a friendly ally that knows they were charmed ... well given a lot of "ifs" a caster can surpass the fighter. Then again, if I wanted to be super skilled in out of combat that wasn't a caster I'd play a rogue. My first D&D 5E PC was a fighter/rogue just for that reason. With skilled and A wizard generally has to choose - are they going to be contribute to combat or out of combat; I've never seen one that excelled at both.
I never had an encounter in a non-magic area, although every once in a while a monster had an anti-magic cone. But in most session the non-casters contributed just as much as the casters, frequently more. Unless you have 1-2 combats between long rests that's been pretty standard in every 5E game I've played. Fighters and caster serve different roles but there is no way in my experience that wizards automatically contribute more to the effectiveness of the group. Without the fighters to protect them they're glass cannons.
The reason I bring Solasta into this argument is because they provide me with concrete information, actual numbers I can compare. For a while I played a lot of modules, it's kind of a nice half-brain-dead game. The wizard out-damaged the fighter in exactly 1 module where they were given a wand of fireballs early on and enemies were almost always grouped up.
As I said, PCs in my game are 20th level. I don't screw over the wizards, they are free to purchase whatever scrolls they want. The one complaint I hear from the gal playing the wizard? She's generally not as effective as the fighter in combat and if I focus fire on her she gets knocked out of combat quickly. Meanwhile I had another player ask to switch from their high level rogue to play something else because they knew they would always make just about any DC I threw at them because they had reliable talent.
No one class or character, in my experience with multiple groups for the duration of 5E is that much more powerful than any other class. They each have strengths and weaknesses. Absolute 100% guaranteed balance is never going to happen but in 5E it's fairly close.
