The real reason League is more fun with friends is...

... you don't wanna ever get angry with your friends. They are your friends!

It does not take away the fact that too many features of the game tend to make one unhappy when on the losing side. And makes the gaming experience as a whole unfun. Length of game etc.

When Rito encourage us to play with friends... everyone seemed happier. But the main game is still problematic. It's trying to cure the symptoms not the disease. A solid game will hold its own for both solo and team players.