This will not be about the actual gameplay. This will be about the client and the support. You must know that I am nowhere near an expert in the gaming industry, so this will be from the average gamer's point of view.
It seems that there is always a problem with the game. I will start with the most recent one, that started yesterday. I open the client and after about 3 minutes it crashes. This obviously makes playing the game impossible. Other issues I had were in-game crashes (some of them resulting in "leaves" and even warning from the LeaveBuster thing), constant disconnections from pvp.net (which also caused me to miss queues, or worse, fail to select a champion in ranked and lose about 20 lp) or random freezez in champion selection screens or during bans. There is always something wrong with the client. The support is also one of the slowest that I've seen in any game. It took Riot 11 days to fix my problem with purchasing RP. "Fix" isn't even the right word as they basically told me there's nothing they can do and that's my banks fault.
I find the "but it's a free game so problems will exist" argument stupid. In my case, I've spent about 200 euro on services, skins and champions since I started playing 2 years ago. I did this mainly for what I received, but also to support Riot and hope for improvements in the game. Sure, new content and the UI changes are always nice, but technical improvements seem to be unexistent. LoL being one of the most played game in the world (if not THE most played game), I can only imagine the profit they make. But I don't think that this is the main source of income. I'm pretty sure they make a significant amount of money from tournaments and sponsorships.
I understand that they have servers to keep up and running, they develop champions, they have staff and they open servers for new zones. But instead of doing all of this, why the hell can't they fix the already existing servers and the other game breaking problems? As I said before, as LoL is among the most played games in the world, I find this kind of problems unacceptable.