Because honestly speaking, BRD and MCH are both close together enough that they can be competitive to each other. The factor is the fights that design to favor one or another (which has been the case since 2.x, and has nothing to do with job balance honestly, espesically when the two are interchangable). You can look at the logs right now and see that the top BRD/MCH are actually by the same player, and the instances where the MCH does more has numerous factors from clear times to buffs that are in the MCH's favor (specifically the absence of an AST)
What? Did you even look at the fights? I'll grab an example right now with A5s. The top MCH is at 1,740 with a 4:30 clear time, the top BRD (who happens to be the same player who is the top MCH) is at 1,630 with a clear time of 5 minutes...but the latter doesn't have an astro. The second highest BRD would be around 1,580-1,600, also doesn't have an astro, and the fight took 6 minutes which is going to lower the overall measurement of dps as the fight drags on. The trend continues on and on, and at that point you're comparing the dps of a BRD who probably has it as their clear attempt versus a MCH who has it on farm. You keep bringing up the 200 dps difference, but don't see why it's there, but instead assuming that MCH is straight up better than BRD from a dps standpoint.
Your summoner has miasma, miasma II, while blackmage has blizzard and lethargy. Even if you were to take in a BRD, your group still has means of putting out heavy, which isn't on cooldown. The balls also spawn in intervals from each other, you're not delaing with 6 at the same time, and melee stuns are more than enough. I won't disagree it helps, but that's going into fight mechanics that favor MCH (which can round about to having fight mechanics which favor having a BRD, like say having cleanse debuffs). The solution is not to homogenize the two jobs just for something like this, because something like having a stun of 2 seconds when your party is capable of doing at least 4 stuns of equal/longer just by the offtank and melee dps by itself isn't going to be the huge factor of clearing brawler. Not to mention BRD has more higher potency oGCDs at their hand that makes it easier/more ideal to shoot down adds, as well as the cooldowns that also helps in that regard (because wildfire is entirely useless for something like this)