Your "evidence" is false.
Gun crimes in the UK have not changed substantially since the handgun ban of 1997, and in fact in 2003 the number of gun crimes was nearly double that of 1996, the year prior to the ban.
Statistics show that gun crime rates remain flat, or actually increase following gun restriction, depending on the country being examined. Most researchers have concluded that there is no demonstrable cause and effect relationship between gun crime and gun restriction laws. In other words, the latter has zero effect on the former.
The statistic that does actually drop significantly following the enactment of gun restrictions, is suicide rates. Suicides account for nearly double the number of "deaths by gun" than homicides.
You want to focus on mass shootings because of Texas and Las Vegas, but let's not forget all the vehicular massacres and bombings. What are you going to ban to prevent those?
How about we not react emotionally and ban this or that in a futile attempt to prevent tragedy, and recognize that this kind of thing is going to happen, you can't stop it or prevent it, the best you can do is mitigate it. And the best way to mitigate it is to have more people ready and able to RETURN FIRE when these things start.