We grant limited monopolies on created works to incentivize the creation of the works, but that's it. There's no deeper moral grounding. Words you put out into the world don't belong to you anymore; they created impressions in the minds of other people and those impressions belong to those other people, by natural right.
You're right that it's just as sound a property right as every other, but it's one that cuts remarkably against the grain of the underlying natural rights (for a specific perceived societal benefit), and it should always be evaluated as such.
Every generation should be asking "Does the current copyright regime create more good than harm?" And every generation should correct if the answer is 'no.'