It won't. Thats not how capitalisam works. If high quality data became unavailable, then companies will be created to fix the problem. Only they look quite different from NYT.
Just like how Torrents didn't kill movie industry. These are lazy arguments made by people who want to make money through lawsuits.
Also I can guarentee you even in worst case, humanity would survive just fine without those high quality content just like it did for the past 50K+ years.
What you should actually be concerned about is stupid law suits like this that can prevent progress.
AI could help humanity solve more pressing problems like cancer.
By getting caught up in silly law suits like this and delaying progress one can make a case that you bring more suffering to the world.