A basic point is....how healthy is your parent stock? If you start with birds that have issues---they had to be assisted to hatch, they developed poorly, they're not especially productive, they're finicky and frail and need coddling.....doesn't really matter if it's one generation or 20, those birds aren't going to do well. Start with good, healthy stock and you'll have good healthy offspring, for the most part.
I think that's the misconception with comparing to human royal families. Their issues weren't necessarily from inbreeding for generations, it was because they were wonky to start with.
The inbreeding/linebreding just emphasizes whatever is present, be it good or bad. The more generations, the more emphasis you'll see. Good or bad.