Why doesnt each class get their own limit break effect?
Because that would very much encourage class stacking and/or very specific group comps. You fail to realize that different LBs would have to function differently and do different amounts of damage and have secondary traits. If MNK has the best single target DPS LB then every party will have a MNK and give the middle finger to DRGs, RDMs, BLMs or other DPS.

The current system's emphasis on role ensures you have that particular role covered while also allowing for variety in parties. It's one less thing that may give parties the excuse to stack classes or exclude certain jobs, and that's always a good thing.