Riot's code base has a massive amount of technical debt, to a point where a rewrite is likely the best choice because of past technology decisions.
Anyway, it would end up being called a sequel.
A team that 'made a mess' may think they know all the mistakes they have made in the code, but they have never proven it, and they haven't been practicing doing things 'the right way'. They haven't even learned how to push back on bad strategic decisions that made things worse.
How do you know that the rewrite will be profoundly better than the current version? I think you have rather a lot of evidence that it won't.
Take a team that cleans up their messes as they go. They know whether their new ideas are better or worse. They have proven they 'deserve' a better code base by building one. By the time they know for sure what's really wrong with the code, they no longer need a complete rewrite. They need a partial rewrite that they can string out over the course of a couple years.
If any of that is true, then the people who want a do over won't take advantage of it, and those that would benefit most wouldn't feel comfortable doing it.
They have the most popular video game of all time and you think that a poorly written client is killing them? It has had some problems over the years that are annoying to users (and frankly embarrassing when compared to DOTA 2), but at the end of the day the quality of the client is insignificant to most players compared to the fun-factor of the game itself, as proven by their unprecedented success.
I play League a lot. There are bugs, sure, but altogether the game feels very polished. Much more so than many other games I have played. [There were two high-impact bugs in the current tournament that go counter to this, but they've been addressed already.]
The 'hard way' you espouse is ludicrous and far from the best way. It's not even an option. (Of course this is just my hunch, but it's a well-founded one)
[The ways that league does not feel polished are not related to code quality. They're much more around the new user experience and the toolset available to hardcore players (replays, sandboxes, among others).]
"Murdering them" how?
Continuing to develop while totally rewriting the core leads to wasted effort and a "running to keep up" effect, though allows for a strong technical foundation, provided you actually finish it. Incrementally rewriting the codebase takes longer, but is easier to do in flight, and easy to test in a modular fashion -- and that's already happening.