While Netflix in general is accessible in Incognito/Private mode, they refuse to load their player in this mode, asking the user to restart the session in regular mode. If you look for the technical reason, you find it in multiple FAQ entries:
Turn off private browsing, sandbox or Incognito mode
Private browsing, also called sandbox mode or Incognito mode, prevents Netflix from using cookies to store information needed to stream video from our service. It may also force the Microsoft Silverlight plug-in used by Netflix.com to install every time you launch your browser.
- Netflix support
As for the Silverlight logic, nowadays it's blocked in most browsers anyway.
This leaves us with the logic of cookies. But doesn't privacy mode store cookies just as usual and then simply deletes them when the browser gets closed? In other words, no different than manually deleting cookies. That is, an internal computer action which shouldn't concern a third party.