That was the theory.
Depends if you're talking about nova, white room or a real campaign.
2024 I'm not convinced but I'll get back to you.
I have played all of those classes (2014) in 1-20 campaigns. Fighters are not the king of melee in play.
I will note I played capable Melee Bards and Warlocks to 20th level, but I have not played a melee-optimized Bard or Warlock to 20th level. But I am pretty confident I could and still be very good at the social pillar.
I have played Bladesingers optimized for melee and IME they are in a class of their own when it comes to melee in tier 2+ (but still less powerful than a traditional Wizard that is going to cast things like Wish, Simulacrum and Forcecage).