Mitzvah War

As I understand it, the concept of a mitzvah war is a war that is waged for the sake of some mitzvah, such as conquering the land and annihilating Amalek. The obligation to fight is by virtue of a Torah command. On the other hand, helping Israel out of trouble is simply a war to save itself. Even if the Torah had not renewed it, the obligation/right to wage such a war would still exist. Indeed, as far as I know, the Torah has not renewed such a war anywhere. It is a simple understanding that every people has the right and duty to defend themselves. Maimonides (1 Kings 51) includes this war in the list of wars of commandment because in it too there is no need to seek permission from the Lord (see the same title). Furthermore, if we do not have a king and our lives are in danger, is there no obligation/right to wage such a war? And see there in the 6th chapter of the Book of Exodus, which mentioned as wars of commandment only the war with Amalek and the seven nations, and not the help of Israel from a time of trouble.