Yes and no. BRD had an MP restore song that was mostly for recovering the healers from disaster, because it competed as an MP spender for them with Foe's Requiem, which debuffed enemies and made them take more magic damage. The Ewer recovered MP which was nice if you needed it, but you couldn't plan around its use. Otherwise, the MP situation was oddly similar to how it is now, for different reasons. Aetherflow restored 20% of maximum MP, plus the recovery from Energy drains meant Scholar had functionally infinite MP. AST had Luminiferous Aether which functioned like Lucid Dreaming (plus some terrible threat management attached) that they could extend with Celestial Opposition. Combined with their lower MP costs across the board, AST also functionally infinite MP unless things started going really far south. White Mage had Shroud of Saints (Lucid but with fewer ticks and a good threat dump attached) and Assize was still a fantastic ability, but MUCH weaker than it is today. It was 300/300 heal and damage potency, you had to effectively choose between the damage and heal with Cleric Stance (so it was basically only a damage tool without the bonus heal effect), it restored 10% MP but was on a ridiculous 90 second cooldown. White Mage, you're gonna love this, was the only healer that bled MP just from maintaining their basic rotation with nothing they could do about it other than hope for Ewers from an AST cohealer or a pity Mage's Ballad from the BRD.
Huh, weird, WHM was the only healer that was MP negative from its basic rotation? We really do come full circle with this job design I swear. WHM's MP economy was overcorrected in Stormblood with Thin Air, several cooldown reductions to Assize (but nerfed MP recovery in exchange. The recovery is effectively the same, but more frequent so it's less punishing if you die). Shroud of Saints benefited WHM from becoming the role action Lucid Dreaming because it had an additional tick. And now here we are in Endwalker, they smacked down one of the major changes they made to rescue WHM's garbage Heavensward MP economy and...we're basically back to garbage Heavensward MP economy, because they fixed nothing else about it since then.