Why are the bash -n and -z test operators not inverses for $@
"$@" doesn't do what you expect. It's not a different form of "$*", it expands to the quoted list of arguments passed to the current script.
If there are no arguments, it expands to nothing. If there are two arguments a and b c, then it expands to "a" "b c" (i.e. it preserves whitespace in arguments) while "$*" expands to "a b c" and $* would expand to a b c (three words).