OP doesn't care about advice.
BLM/Thaum is not a toolbox. They have one tool. It's a hammer. You hit things as much and as hard as you can. (Post 40 none of your other spells work anyway-which is stupid, I agree).
Sleep doesn't work. Lethargy doesn't work. They literally do zero things besides waste time as enemies 40+ will resist them, all the time. So it's not even worth crutching on them at low levels as it will just make you a worse player.

OP, The reason your group dies is because you don't kill things fast enough, draining the TP and MP of your party members as they have to make up for the damage lost from you.
At Level 60, B1 does 600 damage, F1 Does 1400 damage when pumped with AF3. They have the same cast time. So with your "playstyle" the other team members have to put out 43% more damage EACH to just keep pace. Even more if you are swapping Blizzard and Fire. As your Fire would do 300 damage instead of 1400 your way. (I realize the actual numbers are different at your level, but the %change will be the same). So you were too hard for your group to carry.

I'd be frustrated too playing with you. Transpose will fill your mana in 6-9 seconds. While it's filling you can cast Blizzard.

Sadly BLM do not have utility. They are single target nukers. Decent group AoE. They are not healers and they are not support.
If you want to play your way, without trying to get better (running with Full->empty->Full mana) just find your own group with PF and don't subject your playstyle on innocent DF people.
They didn't do anything to have to deserve to play with someone who is purposely not helping.

Advice on jobs going forward. Try and figure out what you're supposed to do as each job. Then read about them. How best to do them.