Game Balance NOW says that every character must be of equal power at every level or the game is broken and bad.
If level isn't a consistent indication of power level comparisons between two characters, then it's not very useful.
Level should indicate level of power, not class. Class should determine type of power.
Back in 1E (and 2E) some classes were just inherently more powerful than other classes because, simply, []that's the way it is[/i] in the fantasy novels and myths and legends that D&D comes from.
One might say they were inherently more powerful because of designer bias (tons of "old school" designers seem to be of the "wizard uber alles" school of thought).
However, a good deal of the fiction that D&D is supposedly based in didn't have magic-users make everyone else obsolete. Hell, Conan faced spellcaster and usually kicked the crap out of them, despite being a beefcake.
Why in the world should Fighters be just as powerful as Wizards?
Because it's a game and one player shouldn't be immediately more or less powerful than everyone else based on the type of character they want to play.
Does this not fly in the face of the genre itself, that a sword swinging warrior face down any menace that a mighty archmage can do?
No, it supports the genre, which is full of non-spellcaster characters overcoming incredible odds and kicking the wizard in the teeth.
What has become of the moment in the story where "Swords are no more use here;" the point when it becomes obvious that it's down to the sorcerer calling on his deepest magical reserves to do battle with the noisome eldritch obscenity which mere mortals can do naught but quake in fear of?
You mean "What has become of the moment when I tell everyone not playing the wizard to roll up a wizard, since their rogue/ranger/fighter/whatever is now useless because I have a hard-on for spellcasters?" Hopefully, the rogue shivved it and it's lying in a ditch, quietly bleeding out.
Then recreate it. 1e is available on the net. There are communities out there that still play it. Have fun.