If clicking 'no' is effective, it raises the question of why can't that just be done automatically for me by my browser, sparing me the obnoxious nag screens
Because it's in the website owner's best interest to make the rejecting process be as cumbersome and annoying as possible. The whole thing is a show of bad faith.
- Persisting a shopping cart. - Storing your login session. - Identifying the node that should handle your requests.
Site operators are forbidden by the law from using essential cookies for tracking purposes.
If a site operator is classifying tracking cookies as essential, or using their essential cookies for tracking then they are very likely acting in violation of the law.
Without it the user cannot know whether an app or website will track them without first visiting it. The act of loading the site can expose the entirety of your browsing activity to the site operator. Whether you would have agreed to those terms or not isn't factored.