Is it just me or are melee classes rendered null by mage classes end game?
I'm not exactly sure what you're doing wrong with your physical setups, but most physical damage dealers should be capable of this unless you're under Low Leverage. The most basic is probably the Pirate/Swordmaster with Two-Handed and Free Lunch. Anything that runs Drain Attack Up and Sword Magic Amp with Two-Handed and uses the Blood Blade for Drain Sword should also hit 9999 easily outside of Low Leverage, and should still be able to hit the cap under Low Leverage after buffing. Anything with Natural Talent/Knuckle Lore should be able to as well, though they trade speed and defense for more support slots and shorter setup times under Low Leverage. A Ninja/Spell Fencer or Ninja/Conjurer with Hawkeye, Precision, and Frenetic Fighting should hit the cap fairly easily (under Low Leverage or not) if you apply their relevant buffs and raise their Hit Count with a couple casts of Quick from a Time Mage, and they'll do almost 80k per turn instead of 40k.
Dork_Vader already made reference to this, and while it takes a little more setup (5-7 actions over 2 turns), a Dark Knight under Low Leverage achieves the highest damage output in the game outside of Bravely Second, thanks to Rage's reduced BP cost. Used properly, it hits for up to 200k damage per round, so you can significantly improve the 250k damage you're doing over 5 rounds with yours. There are a number of setups you can make use of to hit the cap, but let me lay out the one Dork_Vader was talking about in a bit more detail:
Equipment: Ama-no-Murakumo/your strongest Katana, Headband, Brave Suit, Hermes Shoes
-Drain Attack Up Support Ability
-Sword Magic Amp Support Ability
-Two-Handed Support Ability
-50% P. Attack Boost
-Use Blood Blade as an Item to cast Drain Sword on the DK
-Crit buff, preferably 400% or more (Pay to Play, Conjurer's Susano-o, etc.)
*-75% defense debuff on target (optional)
Turn 1, you use Low Leverage, then cast Blood Blade and your Crit buff on the DK. Put up Fairy Ward if you'll be using Life or Death to buff attack (you can cast your P. Attack buff this round if you're using something other than Life or Death for it). You can also cast your P. Defense debuff if you're using one, but it's not strictly necessary to hit the cap. Turn 2, cast Life or Death if you're using it and anything else you still need to. Then immediately begin Raging 3-4 times per round. That's 1-2 turns of setup with 5-6 actions (Low Leverage, Blood Blade, Crit Buff, P. Attack Boost, Fairy Ward, and optional P. Defense debuff) for 200,000 damage per round, so long as your BP battery can sustain it (the Merchant can pitch in with BP Drinks if need be).
Lastly, about monster HP, you're right that most main-game monsters and weak Nemeses have less than 450k HP. However, the Secret Boss in the main game has 715,500 HP and a respawning minion with 67.5k. Strong Nemeses have anywhere from 675k to 1.62 million HP, and some of those have 9999 physical and/or magical defense as well, which forces the use of defense-piercing damage.
Use Sword Skill as a secondary for Dark Knight and enchant your blade (or fists) with Drain, negating the cost of Rage. It'll just keep going and going until a certain cap or the enemy dies. Doesn't work against undead though.
Playing: Bravely Default, Animal Crossing: New Leaf, Magic 2014, Fallout: New Vegas
Shut up and eat your damn lemons.
My level 60 Ninja does 8k damage per BP cold. if I spend 1 BP to cast Quick, that's more like 12k damage per BP.