Black Mage is anything but weak since the rework. Granted you generally are mostly an Ice Mage, with a dash of gap closing people with a lightning Burst move for an additional flat 16K with a guaranteed swiftcast, which can seal the fate of all but the most protected and healthiest players after you've effectively locked them down with bleeds and freezes. Sleep is also far from useless, though not for sleep itself, but rather the extra damage you can inflict if your opponent dares to ignore it, even if they clear that, that means they are now unprotected from everything else you can throw out, so it becomes a matter of timing your flares.
Overall, the real difficulty with Black Mage is understanding the direct correlation to the damage you're inflicting, and why it's being effective. Freezing enemies is obvious, forcing them to waste purify is obvious, and if enemies group up while you get your LB aided AoEs off is a practical death sentence, but often times a player might feel less like they're following a proper rotation and more just pressing buttons and eventually succeeding (if they aren't immediately monk/ninja'd of course, another thing to watch for).
Now, it's worth remembering the BLM in Frontlines is dealing with the Damage Resistance buff being applied to a large amount of classes, meaning outside of your CC abilities and Group AoE, your actual damage is more effective against classes that don't count as melee. Since you require a bit more setup to shine, and in the case of swiftcasting, micro (bless the ability to Aetherial Manipulation in place, good lord), you do inevitably need to put in a bit more thought than other ranged archetypes in this mode to achieve your true potential.
But inside Crystalline Conflict, you are an absolute powerhouse, and only if you are stunlocked and focus fired, you are truly otherewise unstoppable... something which can frustrate many melees because almost everything in your kit is designed to no-sell them getting easy wins as long as you have line of sight, know how to bait them into using their defensives/cleanses, and the favor of this game's server tick system. Your team shouldn't ever let you deal with the consequences of your artillery based design, you are there to cause as much suffering as you can so long as you have line of sight.
So in summary: Black Mage is extremely strong and a high priority to remove from the board. It isn't a one-man army however, and the game doesn't really make it obvious just how effective your setups are, just that *something* is always doing work. That in itself is important to remember, as even if one thing doesn't work out, you have plenty to fall back on. Compared to how it was before the rework, or even during the initial phase, Black Mage is in a really strong position, and if you come up against players who absolutely know how it works and how best to use it: pray.