As a BLM, your statement about us being bad on movement heavy fights, its actually not really true. We have all the tools at our disposal to completely negate most movement downtimes. In fact, our total uptime is higher than melees since we don't have to deal with melee range mechanics/cleaves. We also have skills that allow us to negate oncoming physical or magical attacks (meaning we can choose to ignore things like titan landslide, ADS high voltage, Twintania Divebombs, Twintania twisters and so on). Even on fights with required movement, we have a fantastic 30 sec CD teleport/dash that we can use to move between GCDs. In addition, you can make minor movement adjustments between casts without any delay, by beginning your movement as a cast reaches 85% completion, it will complete the cast as you're moving. Can also move during GCD wastes after fire3 and thunder procs.

So tl;dr bad BLMs have issues with movement fights, good ones plan around it and utilize their skillsets to continue providing uninterrupted DPS.