With the new change of STMRs now activating trust abilities, a good swath of units can benefit from ignoring their TMR altogether. This list is not comprehensive, instead focusing on units who receive at least some kind of tangible benefit. I'm not listing healers and supports due to their gearing not being that tight to begin with, and I'm assuming you're not replacing a good TMR with a better STMR; Akstar is technically better off with Dracu Lasswell's STMR than his own Rush Glove, but you can use your own discretion for these cases. I'm also disregarding very dated units like Lightning; Aurora Scarf is useless, but let's not gild the dumpster lily with Omega Weapon.

The candidates

SophiaSophia: Sophia is a DH mage, and Stardust Rod has significantly higher base MAG than her TMR. Would be a no-brainer, but you are losing access to the doubled counter chance and refresh tied to Crescent Rod, so be wary if her MP consumption is already troubling you.

Lila Lila: Trust bonus is awesome, and she'll be wanting Sledge Tonfa or Amber TMR regardless. Do it.

BalthierBalthier: Would be as above, but he's getting 100% DH from trust bonus, and not TDH. Jerk. Still a no-brainer for the other passives if you're already using guns.

TianaTiana: TMR is pretty crap with a strong trust bonus. Easy decision.

FaytFayt: Similar to Lila in that he has a 1H TMR weapon when he'd rather be using a 2H one. Soul Sabre (or Daybreak) shines here.

WilhelmWilhelm: More variety in shield selection is greatly appreciated considering it's a high value slot, and Shield of the Empire gives no resists. Same basic deal with the other shield TMR tanks (Gladiolus and Basch)

ElfriedElfreeda: You weren't using her for damage anyway.

SoraSora: Trust bonus is tame and you're not going to be using the TDW from his STMR, but it's still easily worth it given that Kingdom Key is kinda dumb to begin with.

EllyElly: Like Sophia, but Elly can reasonably go dual wield. If you lack MAG DH gear, Elly will probably end up using Psycho Rod with Stardust Rod anyway, but otherwise: it's spicy. Same basic deal with the other rod TMR mages (Emperor, Livid Shantotto, Lulu)

Mercenary RamzaMercenary Ramza: Frees up a slot for better tank gear, including better access to evasion. Demon Rain and Chow are in similar boats.

Dark Mage GolbezDark Mage Golbez: Given his horrid MP consumption, dropping TMR for a Distant Promise or Artistic definitely helps.

SephirothSephiroth: More of a sidegrade, but Muramasa's additional killers and flat ATK can make up for losing Masamune's doublehand, depending on scenario and your gear.

A2A2: 150% DH from trust bonus is really hot, but be warned that like Balthier, it's specifically DH and not TDH: tough luck if you wanted to exploit that 2H Excalibur, but it's good for other elemental greatsword usage.

2B2B: More ATK in a DW build from Muramasa in a DW build if you're going for that? Not ideal for LB damage and doesn't help her breaking, but it's there.

KurasameKurasame: Useful for longer fights where using a 2H non-elemental weapon becomes a liability due to imbue being on a cooldown.

BarbaricciaBarbariccia: Only if you're not up against human/beast/bird/stone foes, of course.

Trance TerraTrance Terra: She's looking dated now, but this is one way to address her MP cost issues. Dualcast from Soul of Thamasa is situationally handy for Full-Life and Curaga though.

CG JakeNameless Gunner Jake: 30% ATK hype. Mod boosts to his skills don't matter too much when LB burst is his gimmick.

FryeviaFryevia: Move over, Jake, Fry gets 30% ATK and MAG. If you're just spamming Frost Flower Blitz, Soul Sabre is likely the weapon of choice.

DragonlordDragonlord: Losing refresh kinda sucks, but do you really care with all that MP? More importantly, are you really using Dragonlord still?

EllesperisEllesperis: It doesn't matter because her mods were mediocre on release and laughable now. Just killing the meme.

P.S.

Let me know if I'm missed anything noteworthy, and I suppose I could add you to my list.