Copyrights aren't actually about making money with intellectual property at all.
Yes, copyrights allow you to stop people from making money by selling your intellectual property, but that's tertiary to the main purpose.
If you allow others to use your intellectual property without acknowledging that it is your IP, or if you allow others to create a product that utilizes your IP and distribute it without it being regarded as fan-made content, you stand to lose your IP rights over it. If that happens, anyone can sell your product and there is nothing you can do about it after that happens. It becomes part of what's referred to as "Public Domain".
So if Riot WERE at risk to lose their IP rights over LoL characters, they WOULD, regardless of backlash, defend their IP rights and take down the site. Especially since, if LoL characters became a part of Public Domain, people would likely recreate LoL (since nobody is satisfied with Riot's directions game-wise) and sell it themselves. And Riot wouldn't be able to do anything about it after losing their IP rights. Think DotA->DotA 2, but over game design direction instead of recreating a dated game.
However, they are not at risk, as these are informational sites about their product, so they will not take down the sites to defend their IP rights. But I promise you, if they were at risk they would remove them immediately. PR pales in comparison to the importance of IP rights.