No one is worried about cookies, as they are just one and zeros on a computer. It is the personal information being shared with sponsors, social media, analytics, and other vendors or what ever they feel is offering them enough money.

The reason we are in this privacy hell is the confusion between technology, ie cookies, and personal information, ie sensitive information about people and their lives that get traded like commodity goods. It is how technology is used that matters.

The cookie is just an implementation detail. Agreeing to the terms of the average cookie wall will let the website in question capture your IP address and browser fingerprint and then sell on that information for combination with other data sources.

There are many finger-printing and tracking methods of which cookies is but one. A couple of them can effectively “break” the private/incognito barrier (perhaps with less accuracy and/or precision, but given enough data-points discrepancies can be averaged out).

Though some news sites detect private mode and block the article. NYT for example.