I think framing any non-emergency savings as a “privilege” devalues the meaning of the word. If anything can be classified as a “privilege” if it’s not considered a “necessity”, then the word has lost its original intent.
What happens if I have the money to have a fuck off fund but choose to spend it on something else. Is that a privilege? That’s a more interesting topic of debate. The means to build a fuck off fund may or may not be a privilege, but the fuck off fund is decidedly not. At that point, you might as well declare wine to be a privilege.