I can see practical difficulties extending that policy to allow common citizens to do the same, but they are solvable problems.
In my area, we have DAs who refuse to prosecute car thieves because of "disparate impact" on minority communities. It should not surprise anyone that we now have the highest rate of vehicle thefts in the country. And the thieves are getting increasingly brazen and increasingly violent. Something has to give here.
I am sympathetic to the man who chased down the car thief and killed him. We will see a lot more of that in the future if DAs keep letting thieves go without prison sentences. And we will increasingly see "not guilty" verdicts when the DA is foolish enough to prosecute theft and robbery victims who retaliate against the perpetrators.
It isn't a good idea if we want "Rule of Law".
The laws vary by State, as we all know. When I was a cop in NYC, for example, you could only shoot a fleeing felon if he was using deadly physical force against you or others (shooting over his shoulder while running away).
Any rights or authority the uniformed public servants have are delegated to them by, and originate with, We the People. Morally, we reserve the right to take them back into our own hands. As a juror, I will not indict or convict a citizen for taking out the trash.