There's a simple solution. It will eliminate scoreless ties and virtually all ties. Raise the points for a goal to ten and give one point every time an opponent is last to touch a ball that goes over its own back line. The corner kick will still be rewarded.
With those rules a typical 1-1 tie game would wind up something like 17-15. Defensive and offensive strategies would become for more complex and the game would become far more interesting.
When I was in the States at a baseball game I mentioned this idea to a soccer fan from South Africa. What was his response? He opined that baseball would be greatly improved if, instead of ejecting players, they were given a yellow card at their first offense and only ejected if they got a second.
There's no talking to those people.