I think the one word that sums it up is ‘safe.’ Few people would be willing to spend millions developing an app, then risk it all letting someone express themself. The NYT lower stakes lets them be better.
On the other hand, an app's interface is something the users look at for a much more extended period.
To compare with newspapers, think about the web interface of different newspapers (or even the layout of most print newspapers) -- you'll be amazed at how similar they are! I just looked at: https://www.nytimes.com/ , https://www.washingtonpost.com/ , https://www.bostonglobe.com/
So, while I would like more variety in interfaces, I think it's a very hard problem.