I think it's also because the game modes are cheesy. I mean, cheesy on purpose. Cheap thrills are their appeal. But for the average player, cheesiness isn't a satisfying long-term source of entertainment. Think about Mirror Mode.
The first time you see the enemy team aced by 5 cannon barrages, it's really cool and fun. But the 3rd time GP is voted as your mirror mode champ, your reaction is, "Not again! :S"
They make game modes unavailable, to keep them fun to play.
There's also the technical side of things: any new game mode, especially those that rely on cheese, are going to have something weird in them.
That leads to a bunch of design challenges, to make sure the game continues to make sense: Should akali be able to stealth in a friendly akali's shroud? What about an enemy akali's?
It also leads to a bunch of technical challenges, which means a bunch of bug fixing.
These things just take time, if they're going to give us quality content, which is why we can't have a new game mode every day, if you want them to stay as cool as they are.