How is something beyond the power of the full force of government different from an inalienable right?
It isn't an inalienable right for the same reason that committing any crime isn't an inalienable right. Jury nullification simply can not be prevented. Saying that this makes it an "inalienable right" follows the same logic as "you didn't break the law if you didn't get caught."
If I murder someone and get away with it, in spite of the efforts of the law enforcement agencies assigned to the case, that doesn't mean that I had a "right" to do whatever I did.
Reality check, by the way: this entire thing is academic anyway since we both seem to admit that jury nullification can't be prevented.