Uh yeah they don't? Unless you also have problems with words such as über, façade, señor or crème brûlée.

Rather, the removal of them affects readability in a similar way to removing accents, punctuation or writing in all lowercase.

There are two types of diacritics, from the perspective of any reader: the ones they are familiar with and understand, and the ones that are visual noise. American and (West) European audiences are typically more or less familiar with the umlaut, accent, cedille and circumflex mark, and the tilde. Other diacritical marks typically fall in the second category for them, outside of use in their own language.

So expose the reader to them until they become familiar, problem solved

so just ignore the "visual noise" or "random scribbles"? i dont get why youd want to remove meaning from an article simply because you dont undestand it.

For the same reason you choose one font over another: the aesthetics of a text matter, especially to publishers.

Now, I should add that for an article that is specifically about language, and even has some illustrations of the meaning of these diacritics, this is almost certainly a bad choice on the NYT's part. But as a general rule, I think it is defensible.

Well, I disagree that simpler means better looking. It's akin to arguing that a commie block has better æsthetics than a gothic cathedral.