However, I think one of the brilliant things about Iron Dome is the fact that it doesn't try to shoot everything down. If a missile is determined to not threaten anything, it is allowed to crash on its own.

That may not be as big an optimization against opponents with good aim, but the people who fire rockets at Israel are often using old equipment that they can't aim well.

Iron Dome isn't comparable. Iron Dome is made to shoot down short-range rockets and shells. It makes intercepts against slow moving targets at low altitudes. It would not likely have much success against a mach 5 Scud that would spend only a few seconds within Iron Dome's engagement range before impact.

Iron Dome is vastly superior to Patriot in one key area, namely cost. Shooting down cheap Palestinian rockets and mortars at $2 million/missile for Patriot would not be feasible, but at $30-50,000/missile for Iron Dome is completely doable. I don't know what Patriot's success rate would be against these targets, but given its cost, it doesn't matter if it was 100%, it still wouldn't be workable.