Why don't they, there have been lawsuits over just these behaviors in the past. Hell, even the multiple representations of the picture in computer memory have had to have allowances.

Copyright is a gigantic fucking mess that the US has forced over a large chunk of the world.

You might be thinking of fair use, but that's an affirmative defence. Every time someone has copied someone elses artwork and modified it into a meme, that's copyright infringement and remains so even if is eventually ruled as fair use. If you make a fair use claim, you don't deny infringement, you make the claim that you were allowed to infringe.

Try replacing "picture" with "music file".