There is a practical consideration: the rural areas in which so much crime in high-crime red states occurs are almost impossible to police in this manner. Too spread out to have the intimidation factor of armed troops work, too long a response time to actual incidents. Basically the same problems legitimate rural law enforcement always faces...

Also, those high-crime red states rank that way on a per capita basis. The high overall crime numbers obviously derive from urban areas (y'know...where the people are...). And yes, while there are red cities on the list, there are more blue ones. Mind you, that difference has less to do with the political affiliation of city governments than other sociological and demographic factors, but it makes for a popular (if puddle-shallow) talking point.

Which of course leads back to what you already mentioned: this in part about politics. "Getting tough on crime" has been a big part of the conservative election handbook for many decades. And there are other factors at play...