You forgot the "save it to my machine" part which lets me view the picture whenever I want without visiting its creator's website repeatedly. This means I don't need to be exposed to ads, which in turn lowers the creator's income. It also means other people can get the picture from me rather from the creator. Even less ads and payments.

Obviously the creators want more money and control. Thus copies are only allowed to be made if it benefits them. Viewing a copy of the picture via the website might be permitted, but saving it or sharing it might not.

The truth is nobody really cares what creators want. People will save and share and edit and meme it all up because they can. It is natural. It is their delusional belief that they can control what others do with information that is out of touch with reality.