I've only seen the first movie and none of the sequels/shows, but by the time the first movie took place there were supposed to be VERY FEW immortals left in the entire world. Remember, Sean Connery was only around in flashbacks. The whole "There can be only one" thing had mostly weeded them all out, the "Gathering" was supposed to be I guess like a championship tournament to determine the last survivor.
I know that the stuff after the first movie introduced a lot more immortals, but if they reboot back to the concept of the very FIRST movie, then super-powered sword fights in the streets of modern cities should be pretty rare.