Fights in this game already last a long time compared to the other games in this genre, so if you think they're quick fights now you'd be in for a surprise if you ever play HoN or DotA.
Champion builds are the way they are because, generally, they're the most optimized version of what that champion needs. If they need a lot of AD, then they're going to build a lot of AD. If their one skill that scales with AP is pointless to get AP on, you won't see them build any AP at all unless that AP is a byproduct of picking up some other item. Purposefully building sub-optimal item choices for the sake of "dragging fights out" is just not a good idea in a competitive game. Maybe if you only ever played by yourself against bots you could get away with this, but you're in a game with 9 other people, and all of these people want to win the game. To win, they're going to try to build only the good items their champion needs to perform.