Besides BLM's gimmick IS blowing off their MP then having a literal cooldown period while they gain it back, it's especially based on managing that currency with all its resources. If you took out MP you'd have to add charges to Fire IV which would get consumed and force you into Umbral Ice to regain them, and it'd make BLM's rotation even more set and unforgiving and... kind of boring (Use Fire IV 3 times because you have 3 Umbral Hearts, then use Bliz 4 to get 3 more UHs, then spend them on Fire IVs, repeat, where does Despair fit into this? idk).

Right now a BLM has to juggle their AF timer with Fire IV/Fire/Fire III, they can use Manafont every 180s to squeeze in more Fire IVs+Despair and that resource management widens the gap between a decent and a great BLM. Without MP, Manafont would need to be reworked to instead give "Fire IV" charges or whatever. Without MP, BLM would suffer the most as its whole kit would have to be reworked.

For the other Casters it's more of a punishment for bad resource management or dying (if you die as a RDM and don't have Lucid, you'll be stuck casting one spell per tick until it comes off CD, SMN is... more forgiving with Egi Assaults and Ruin's low MP cost and aaaall its CDs). And on healers it's really a punishment if other people die, or you're spamming your big heals like Cure III (looking at YOU, Terminal Velocity, 2-3 deaths during Triple Apocalypse and we're guaranteed to wipe because healers won't have MP for the heal check).