When I said that I was really weighing the true benefits of turrets versus songs. What Angary said is very true, that with Hypercharge and turret placement you can get MP back super quick. The downside to that is that you're blowing one of your best offensive cooldowns on a defensive side of thing.
The equivalent is Battle Voice, which is always a benefit whenever it is popped. Be it for extra Foe's damage off the bat or increase mana/tp recovery for the party. The downside is that BV doesn't affect the bard who sings it. That's not always a downside. In the niche scenario where I just get rezzed, have no mp, and healer is out of mp as well, yeah, battle voice isn't gonna help since you'll end up losing about half of the duration of the buff or something because you only have like MAYBE ten ticks of MP regen before you're OoM. In basically every other scenario that exists Bard has it better than Machinist when it comes to spot MP regen.
Even when Angary mentioned that you can drop a turret and Promote/hypercharge during a burn phase to get MP back, it's still, in my opinion, way worse than Bard throwing up a single GCD.5 to get ballad ticking for as long as you need it to. You're impacting your dps, sure, but you also aren't burning an cooldown in a defensive manner where you may not need the full duration of it. If you turn promotion off during single target burn phase you still now need to swap your turret and lose your Hypercharge. Bard just shuts off the song and you're back at full damage potential.
Basically, the switching is incredibly faster and much more auto pilot than turret mana/tp recovery. Foe Requiem also lasts far longer than Hypercharge Bishop turret does and you have it up far more often than every two minutes.
Turrets are also usually counter intuitive for the situation at hand in regards to their Promotion abilities. Typically you will have Rook up to deal with a single target situation, but if you need MP you need to swap to Bishop and promote it. Regardless of how easy and seamless this can be, it's still two button presses between gcds to activate. When MP regen is done you now need to recall Bishop and toss Rook back out. Only one action, sure, but it still requires you to place it somewhere which is a lot more than Bard has to worry about when literally clicking their song off.
Rook's promotion is only really useful in AoE intensive segments when you burn it quickly. However, in an AoE pull you want Bishop activated instead, so if you need TP you need to take time to set up bishop and slap on Promotion. You can attack inbetween these movements, sure, but it still requires more steps than a Bard clicking a song and it's up in 3 seconds. The time "wasted" is equivalent even if MCH gets off one more GCD, you're weaving in support between that GCD where you could, in theory, be weaving in offensive cooldowns or anything else. It's still a gain on the MCH side at the cost of being slightly more bothersome.
TL;DR
Bard
+ Songs switch easily, less micromanagement
+ Foe Requiem lasts longer
+ Battle Voice is always useful for any song you're singing, even if you switch songs
- Lose a GCD.5 for singing a song
- No physical Foes
MCH
+ Potentially less DPS loss for support
+ Physical Foes + Magic Foes
+ More flexibility for support more often
- Micromanagement of turrets
- Reliant on Hypercharge for flexibility
If all you have against Bard utility is losing that GCD.5, you're really focusing on the wrong points. As a BRD/MCH you're there to be a battery when needed, which means your DPS takes a back seat during not-a-burn-phase. That goes for both classes. MCH does feel a bit better in blowing Hypercharge during a burn phase on tp/mp regen, but in a practical sense I think people can agree that using Hypercharge offensively is quite superior than the boosted recovery options. That being said, Hypercharge being used defensively is a good option as well. You need to assess the situation and react accordingly. That is what MCH is predicated on for me, and it's really fun to do so.
Again, I play both MCH and BRD and I feel I understand the two classes relatively well. I don't really prefer one over the other and I see both with positives and negatives. I also wouldn't rail against people for their preference one way or the other at all, and all joking I do towards people who shunned BRD for MCH is in jest, because really everyone should play what they enjoy.