Imagine every single publisher does this and how many security holes that will open. Sure maybe you trust NYT to generally do the right thing with data (very debatable) but what happens when Buzzfeed does this? Do you think they'll adopt sensible data collection policies? What about the S*n?
What about the data they collect? Can we guarantee that they simply won't become data brokers again? I would much rather have entrenched players like G / FB collect and take the blame for privacy misses than have every single organization build their own leaky data collection systems.