I really think the core of the problem with PvP right now is that FFA (free for all) is the only option. Some of the biggest problems with FFA:

1) You lose more. Assuming matches are balanced, 3 teams means you are only going to win 33% of games, (as opposed to 50% if it were just 2 teams) this leads to frustration.

2) The "sandwich" effect, where 2 teams battle it out, only to have their efforts come to nothing when the 3rd team comes in to clean up, also leading to frustration.

This is why FFA is the least popular game mode in many other online games. Its fun every now and then, but having it as the only real option is not good.

I think a 8v8 capture the flag would be more sane, and a lot more fun. The 24v24v24 free for all right now is just a chaotic mess full of summoners ><