Surely it does. Including power of arrest.
Arson is not covered by the First Amendment!
A Citizen arresting just (ordinarily) lacks the power to 'transport".
Mayhap you are thinking of the Feudal System of Continental Europe?
Even English Law was closer to our own. Family business since the 1500's after all. England then (Constables, Magistrates, Lawsters, Sheriffs..) , Virginia, later, (much the same..) and/or Commissioned Officers.. but near-as-dammit no gaps to present generation.
Citizenry has the right and responsibility. Arson situation most of all.
We empower Sheriffs and Police Departments to act in our stead.
So long as Civil Authority is PRESENT... and is "functional", they have the con. They may, in turn "deputize" one or more individuals FROM among the citizenry, or, if larger force is required, raise the Posse Comitatus.
County Sheriff would have been within his remit to have DONE that as Kenosha was going up in flames. Sheriffs are responsible directly to the citizenry of their County. Not to the Governor. Nor President.
First act of a new Sheriff in a newly-created County?
Appoint the first Judge. Not the other way around.
Authority?
See Loudoun County, Virginia Sheriff's reaction to the School Board IDIOT asking him for a SWAT team .. and a lot more.
The posturing fool was told-off - firmly. Very! That made the news, BTW. Look it up.
In the absence - or dereliction - of our chosen surrogates, however? Right and responsibility of supporting our society of law reverts to the citizenry.
We hadn't abdicated our rights, after all.
Only
delegated them.
Kyle wasn't the best of examples, no. Wiser, more mature folks should have been controlling. That they WERE NOT is where the tragedy lies.
There should not have been even ONE building burnt, nor ONE person shot.
If the lesson is properly taken, one may hope that NEXT time there will
not be.