Why would an App alienate viewers?
And watching on the Big Screen isn't exactly seamless right now. I open Safari on my phone, open the VoD section on the LCS page, find the game I left off with (because I don't usually watch live), click the link to open it in the youtube app, then hit the Airplay button to push it to my Apple TV.
The other choice is to use the Apple TV remote to type one letter in a time into the Youtube app on the Apple TV to find the game I want, and I still would have to look the name up first on the VoD section.
Riot could make a very nice LCS app that puts access to all the videos in the same place, making it easy to watch them in order. Why would that piss anyone off? If you don't care you just wouldn't use it. I am not saying it should replace anything that is already there, and the App would be free if you did want to use it.
Think of an app that is basically the VoD section of the LCS page on the Apple TV, click the game and it plays. Would be nice if it remembered what you watched already too.
You might not care if you don't have an Apple TV, but that platform is an insanely popular streaming device in the US. If Riot got out the door early with an app it would be nice exposure for them.