I think what they should do to stop PKs in tournaments is allow unlimited substitutions during Extra Time, players can go in and out as they wish, that would eliminate the fatigue factor.
One of the soccer moms on my daughter's team is from Colombia. She says her favorite variant back home was playing pickup without the offside rule. That would really spread the field and open up the offense. But I don't know what it would do to the texture of play at elite levels.