Robert Higgs wrote "Crisis and Leviathan", chronicling the growth of government power through crises. People who want government to grow have an interest in creating actual or perceived crises.

The debt ceiling is used as a crisis to shrink government. Regardless of your goals, if you want political change in our Western democratic culture a crisis is useful.

You're arguing that the supposed decrease in crime is actually an artifact of decreased reporting to police and increased effectiveness in hospital trauma care?

I think that it likely that over the last decades overall crime rates went down. On the other hand some of the change in crime numbers we see is likely through other effects and whenever you have the debate about the subject you should be aware of those factors.

You should always be a bit skeptic that the numbers that you have actually describe reality fully.

Wouldn't attempted murder rates go a long way toward clearing that up?

If you count crimes, counting murder rates has the advantage that if there's a shot dead body, it's quite obvious that a person was killed. There might be some issue with separating manslaughter from murder, but a dead body nearly always triggers procedures in the official bureaucracy.

The same is not true with attempted murder. In a community where the police isn't trusted by the population some attempted murders won't be reported. That's why arguments such as the one linked in the OP are often made via the murder rate.

We do have another tool for determining the amount of crime: Victimization surveys. But they also aren't perfect.