From the perspective of a casual PVE player, I can say the endgame material seems very very haphazard. Until doing a little research I had no idea that the ops were even part of a bigger story line. They seemed like totally underdeveloped one-shots with a few random bosses and no external tie-ins. Considering the Dread Master story line can be completely skipped if not completing every mission on every planet or unless previously aware of their existence and taking an active role in engaging in their missions, the value of ops in terms of lore and story building are lame.
The fp's seemed to have a decent story line but even then with the inconsistency of being able to find a group and the lack of incentive to do them in the right order you only get a grip on the story after having completed them all 4 or 5.
Imho adding an opening cutscene that got you immersed in the story would be great.
there are beginning cinematics/cutscenes for every operation... Maybe you should not just jump in the queue, but look around on fleet, talk to the quest givers etc...
Also to skip the Dread Master storyline completely you would need to skip a ton of missions.