It would be if anyone would have any idea what you were talking about. The point here is that people have a general sense of what "champagne" is, even if the term technically describes a more specific product. Most people have no idea what Sancerre is, and those that do understand that it's a specific appellation, not a generic term for sauvignon blanc (or pinot noir).

To bring this back to the Kleenex example, most of the time people aren't specifying a particular brand when they say "kleenex"--they mean facial tissue. The fact that most people use "kleenex" as a general term for facial tissue doesn't mean that if I ask for Viva (another Kimberly Clark product) that I think that it means the same thing as Bounty. Viva is not a brand that also happens to be used as a general descriptor, and neither is Sancerre.

People (well, most people--apparently many of the exceptions are on this board) are good at using context to derive meaning from words that can have different meanings. This isn't a problem, it's a virtue.