I feel like there should be levels of difficulty next to each jobs name.
Monk would be top difficulty.
Monk isn't bad, Monk is completely viable for every encounter (Yes including Chimaera) It just takes a LOT more skill and a MUCH larger attention span. People don't NOT invite monks because Monks are bad, They don't invite monks because there's a much larger chance that somebody playing a monk is going to be bad and mess up the party.
I've seen Monk top DMG on Every fight, save for Princess.
Now, Think about what you're really asking though: Fights so homogenized that it favors NO class? That would in fact lead to the most boring encounters I could think of. I really enjoy that certain classes have abilities that cause them to shine on a fight, and hope they keep that model. I also feel that did that really well in this patch.
Coincounter: Bards are amazing on coincounter, they do just as much DMG( probably more ) Than your BLMs and have the full uptime that the Melee won't have. They're not game-breakingly ahead but they certainly get to shine here.
Miser: Monk. Fist of Fire. Pure win. Along with that, your BLM has an irreplaceable tool in the form of Sleepga for this fight.
Princess: Warriors/Dragoons. Finally, an AOE fight where things hit hard enough that you can entirely warrant to bring your heavy plate AOE classes. The guard spawning every 1 minute lines up perfectly with lots of their burst skills (Jump, Steel Cyclone)
Chimaera: Black Mages excel hardcore here. Magic Vulnerability+ The ability to avoid all AOE at a range? The physical Resistance makes Bards, Warriors, and Dragoons less viable for this fight. Monk is still the highest DPS on this fight. The last phase it is very frustrating to dodge traps, but if you suceed you are easily rewarded with the highest damage out of any of the classes. I've yet to really test Dragoon on this fight. The increased melee range may make it quite a viable option.
You know the class that should be complaining?
Paladin.
You gave them another Block Ability, and Sanguine Rite. So What? Still not enough. The DMG Mitigation is barely ahead warriors, HP is lower and dmg is maybe 1/10th. Not to mention Warrior with Mighty Strikes is capable of self healing themselves back from empty.