I think that fat turrets just have greater redundancy than any other ship type and that gives them an advantage. For one, they are incredibly mobile. There are few moves they can't pull off. You want to go somewhere, you can do it. You aren't limited by your dial. They also don't have to worry about getting people into firing arc. That's huge and also works well with the first part. Maybe you messed up and guessed wrong where someone was going to be. It's still OK. You can still fire at them (in range and if you didn't bump). Next, they are highly durable. They don't give away points until they are dead dead. If you want to run from the fight to preserve points, you have a great chance of doing that. In fact, you can run very well and still fire at them!
It's not that they can't be beat or that there aren't other good lists out there. It's that you can recover from mistakes much easier than any other ship. So, even if you screw up, you can probably recover faster and better than other ship types. That's the advantage that fat turrets have. Also...these lists can put up a fight against all opponents. Things that defeat fat turrets usually don't do well vs. other types of lists. You might not make it through the early tables to fight the fat turrets if you go with a strong fat turret counter. A fat turret list usually has a decent chance against every other list type.
Well said sir, well said