Believe me, I had the same qualm with res being a DPS tax when I used to play SMN at the end of ShB. I put in more effort than a SAM and was rewarded with notably lower DPS because of devotion (one of the worst raidbuffs at the time) and raise (useless when an encounter is learned). I'm not saying I personally agree, just that I understand from the developer perspective that this is a reasonable way to balance.
In terms of Mantra, I do think it's an outlier for power budgeting, but rather than kneecap MNK I'd much rather every class had a notable utility for the raid (like raise for RDM+SMN, Arcane Crest for RPR, Curing Waltz, Nature's Minne+Warden's Paean though those 2 are significantly less useful) to play around and push out more raid potency when well used.
I will stay on the hill of BLM deserving melee level DPS though. It works around typically more stringent requirements than modern melee and doesn't provide utility. Accessing mobility outside of the 2mins is a DPS loss in a vacuum for BLM (though a logical choice to maintain DPS in that encounter). Really from my perspective following the logic back, I think the other casters lacking these positional requirements and possessing great utility combined make this balance more reasonable. If SMN had BLM positioning and rotational requirements I would fully support it being brought up to NIN levels minimum.
Fire IV rotation always dealt more damage, and I'm glad they're willing to push it more with balance patches. My preferred change would be increasing the transpose CD as this would also curtail alternate lines that rely on either counting or addons to accurately hit mana regen ticks, though this would be a more contentious change. I think that that variety of deviation-from-standard gameplay would be better delivered through nuanced abilities than counting to three.