Privacy is an unlikely reason for them to cut ties with the 3rd party system. More likely, NYT is aiming to become the platform for other publishers.

They are in a perfectly competitive business. Anyone can write, and they do. We are reading this new on Axios, after all. What NYT still has is eyeballs, and as long as they can retain a reasonable system for exchanging eyeballs for dollars, they can recruit more journalists to keey writing.

Keeping their ad system in-house will also stop data-sharing with their 3rd parties, thus at least protecting their business in the short run. They are going head-to-head with Facebook.