As I observed it says "media location", not "library location". What you are instructing is not moving the "library" it is moving only part of it. There is a big difference. If you only copy media to the external drive and then take that drive to another computer iTunes will not display that media unless you add it as brand new files. Things such as artwork may no longer be there, ratings are not part of the media files, nor date added or playcount. You only see those items because as far as iTunes is concerned the library is the iTunes Library.itl file. A split library (which is what you are partly instructing but forget to mention that you then have to consolidate media to the new location) is where media files are in one location and the rest of the library files are in another. This will work but adds complexity to later relocating the files to another drive, using a new computer, or backup.
everything, even more than iTunes needs/can use is in there.
No, it is not. It is critical to make the distinction between a library and media. Think of a city library with a building, books, staff, catalog, etc. Moving only media to the external drive can work but it would be like a brick and mortar library having off-site storage for its books, in which case that storage is not the "library" it is a storage facility that does not have library functionality. If the user's computer crashes the media will still be on the other drive but the rest of the support files will not be on the external drive.