This was true of physical media (books, phonographs, etc.) and is true of downloaded media. You might own a paper copy of your favorite book, but you don’t own its words, and the law prohibits you from making a copy without the owner’s permission. You can transfer the medium to someone else, but you can’t preserve the content for yourself. If the book is destroyed in a fire, you must buy a new copy.
Similarly, you might own your Kindle, but you don’t own the content in it. You can read the content, but you can’t copy it.But there’s a minor advantage of a digital license: if your Kindle is destroyed in a fire, the publisher allows you to read-download the content to a new device.