What if the later writers just got worse reviews because they were in the later seasons? In other words, something else caused the decline so the later writers got worse ratings.
Your wording here suggests that the later episodes were simply rated lower because they were later. However, I think your point is that the later episodes got worse ratings for something beyond the writers. Certainly possible. Even if nothing else changed, it must be much more difficult to write a fresh, funny episode when 200+ episodes have already been done. There were also external factors which might have driven a change in the comedy of the show, the beginning of Family Guy, e.g.
It was the style of celebrity cameos that made things worse. In recent years, the cameos served more to showcase the celebrity, in ways that didn't contribute to the show, rather that utilizing the talents of the celebrity to make a good show, like they did in the past.
You only need to look at the Lady Gaga episode, the worst-rated episode by far (and for good reason) and compare it to any cameo in the first 9 seasons, and a good number of cameos in the next 10.