I have a friend that's an amazing Dungeon Master. While he creates the world and fills it with NPCs, it is definitely a sandbox. We are allowed to do anything we want and he implements consequences and repercussions for our actions.
He has been running the game world for something like 20 years and it's gone from a tech level of the middle ages, to a Science Fiction near gundam level, and then was reset due to a player's actions back to the pre-stone age era. His main plot has always advanced throughout it all and it's extremely enjoyable to play in the world because he has taken the time to build such a rich history.
I don't think the game system actually matters when it comes to allowing and/or encouraging "players to invent crazy, stupid, convoluted plans to dominate the world." That all rests on the shoulders of the Dungeon Master. Some can do it naturally while others require some practice. The key though, I believe, is the willingness to give up some control for your world. That can prove to be extremely hard for some people to do.
I do not like evil characters that target the party. While an occasional pick pocket or running from danger rather than helping might be slightly tolerated the outright attack is no good. I'll tell you why, if I am going to sit down and enjoy a game I don't want to have to worry about monsters attacking and player characters too! Its likely that such a character would have an aura about them so my character would not be in the same party with them.
Oh, yeah. Treachery within the party would be intolerable. Then again, in the Marvel universe, the heroes seem to spend almost half their time beating the crap out of each other until the villain shows up. Maybe that's how they keep in practice.
And I could see a game with evil characters quickly degenerating into a "Look how horrible I can be" Contest, in which the players commit atrocities in order to top each other.
Edited: KenGreen on 24th Nov, 2015 - 11:35am
I think Lex Luthor is a good example of a character that thinks he needs to right the wrongs of the universe and in the process he makes it worst than before. A villain could also be a Robin Hood type where one group sees you as the hero and the others see you as a villain. In that role you take on an alignment like chaotic good.