It's honestly less them not being paid enough and more them not giving a shit. Writers and narrative designers have never been taken seriously in the game industry. There is this bonkers stereotype that unless you can provide a string of code or some "hard" (read - visual or audio) art assets, you are completely useless. It's been proven to be false time and time again with games like Planescape, Pillars of Eternity, Half-Life, Okami and Bayonetta, yet the developers are still convinced that writers are just someone who puts flavorful text into the game.
Unfortunately, because of that, the industry has given spawn to precisely those kinds of people - ones who will write some flavorful text on a napkin and laugh their way to the bank, pretending that they're actually doing work that enhances the game. I'm not saying that is exactly how League's writers are, but that is certainly how they present themselves to be.
Another major issue is that department-driven structure of large companies like Riot is detrimental to writers, who are often simply not allowed to influence the visual and gameplay design. Okami, Bayonetta and Bioshock blissfully went around that by having the director do all the writing and world-building, but it's often very hard to actually be allowed to change things unless you're a project lead.
So really, it's a combination of writers who either don't care or aren't allowed to change things even if they do care, compounded with a stereotypical dumbass marketing team and what looks like very bad management on Riot's part (let's be honest, no team with their amount of resources should have all the content release consistency of a coop filled with zombie chickens).