BRD and MCH actually have two different contributing factors for their lower damage output and it's honestly easier to explain and understand if you know how things worked when 2.0 originally launched.
When ARR first released BRDs had comparable damage potencies to the other ranged DPS jobs on their skills. Their actual weapon damage was slightly lower, however, to compensate for their mobility. Melees had to constantly dodge out of melee range and thus lost damage, casters had to constantly stop casting to reposition and thus also lost damage. BRDs never had that problem. Their rotation was never interrupted by anything so they had lower weapon damage to compensate. The compensation for their utility skills at the time was simply the damage reduction whilst maintaining a song.
Now, when the player base reached the first turns of coil en masse a problem quickly emerged: parties were always taking two or three BRDs and usually only one melee just for the limit break. With multiple BRDs they could rotate songs and essentially maintain infinite resource regeneration for the entire party. For progression groups this was a godsend and trivialised a lot of content since healers could use their spells incredibly inefficiently and just spam the big heals. This also meant SMN and BLM were getting the shaft as parties just wanted to stack BRDs for everything. Why take a caster DPS when BRDs did just as much damage and gave infinite MP and TP to the party?
That's when BRDs got nerfed. Their potencies were severely crippled across the board. The devs needed to make it non-viable to take more than one BRD. The nerf to the job's damage output needed to be severe enough that it wasn't worth stacking them for their songs any more. That is why BRD's do so much less damage than the other jobs. Yes, other jobs have utility skills but I don't think you understand just how game changing it was to have multiple BRDs rotating songs... Nothing compares to the utility a BRD brought. They were that good.
Now with Heavensward out and the new skills I think people are getting confused about how things are balanced. Wanderer's Minuet is a way to give BRDs and MCHs back the damage they lost to compensate for their mobility. They can choose to sacrifice their mobility and get a damage buff that makes up for the lower weapon damage. Now it's arguable that the buff they get from using the skill isn't enough which may need attention, but I see many people thinking that the skill should put their damage on par with a SMN or BLM and this shows a lack of understanding of why the job does lower damage in the first place. WM is not meant to counter the potency nerf they got for their songs. BRD and MCH will always have to do lower overall damage than SMN and BLM simply to prevent parties stacking the jobs again in future.
That's really all there is to it. You can argue as much as you like about how unfair you think it is but we'eve never seen parties stacking other jobs for their utility the way they stacked BRDs prior to their nerf. Clearly parties do not think the utility those other jobs possess is enough to warrant stacking them for it, hence BRD utility is superior by far and the devs were justified in nerfing them to compensate for it.
Wanderer's Minuet and Gauss Barrel may need a buff, and I can understand the players that are unhappy with the new BRD play style but these two jobs will never be on par with the other DPS jobs. Sorry if you don't like the facts but that's just how it is.