Interesting approach to a massive topic. I have no doubt the point won't be missed at all by anyone who comments below.
The most contentious part of the article is presumably the section at the end where he claims there are no great songwriters anymore. Also maybe the parts where he dismisses "indie rock" and rap -- though as far as I can tell everything he says about both is true. Both genres eschew melody in the usual sense about 99 percent of the time, albeit for different reasons.
Two things do seem pretty obvious. One, great songwriters overwhelmingly write their greatest songs early in their lives. This is especially true for '60s-and-later musicians but may also be true in the case of Rodgers and his ilk. I'm not sure. Two, this article functions as a damn good brief history of modern (American) music, if indirectly. If you're trying to sample the vibes of 1900-1990, listening to one song by every person he mentions is pretty much all you need.
In reaction to this I listed some of my favorite songwriters post-Nirvana (basically where his list tails off), but I certainly couldn't put any of them in the same category as his top eight, and I would have trouble putting them in the top hundred, either based on quality or sheer output. Thom Yorke is a sticking point, worth discussing, and I'm sure there are others.