239 cookies set when I opened NYT in Chrome. Yes there is a list, but you delete one at a time. I think that was mentioned by OP.
The rest of the solution is to know which cookie(s) is used to limit the reader.
It's not that simple. Did you ever wonder what EACH of those 239 cookies is used for?
I'm very skeptical of anything the tin-foil-hat crowd raises alarms about. But frankly the extent to which our individual web activity is tracked is starting to creep me out. For the record, I spent 36 years in IT, so I think I sort of understand this stuff.
Take a simple example. Look at the cookies this site uses. There's one from FaceBook.
Somewhere on this page there's a small (often invisibly small) link to an image from the FaceBook web site. Your browser saw that link in this page and dutifully sent a "get" request to FaceBook.
The header of that request contains a ton of information about your IP address and browser. It also contains all the cookies your browser has stored from other visits to the FaceBook servers.
Now, just about every site has a "like us on FaceBook" icon, or possibly an invisible image just for tracking. So FaceBook gets a slew of information about you, and all the cookies it ever sent you, every time you visit almost ANY site.
Basically, FaceBook can now track virtually everything you do on line, whether you're signed on to anything or not.
And it's not just FaceBook. There are lots of tracking services out there. Web sites make money by including those invisible links on all their pages. Most sites have dozens of them. Some have hundreds.
You can start to see why some folks are getting paranoid about it. Personally, I find it more of a curiosity, and just a little creepy. It's become a bit of a game to try to avoid the targeted ads based on my browsing history. Clearing most cookies on exit is easy and goes a long way toward that goal.