Canada has such a law. There are lots of firearms that aren't allowed in civilian hands at all.
You know what our last "terrorist attack" looked like?
Guy runs into high-security building with an 8-round .30-30, gets killed. Body count: 2, including the shooter. This guy couldn't buy a gun to save his life (because we also have laws saying that people with a violent criminal record aren't allowed to buy guns or get a license to own them), so it was probably stolen. This was literally the best he could do: an outdated, lever-action rifle from the 1890s.
Nevermind the fact that this happened two years ago and that's what qualifies as "most recent", the entire incident is a demonstration of the stark difference between what happens when a crazy person shares his pain in a country with strict gun laws, vs one without them.