Because not everyone shares the military leadership's own instinctive reaction against using military as police, let's briefly recap why we don't do that in the U.S., except in rare (and today not applicable) circumstances.
The reasons for not using the military include: hard lessons from history, pragmatic needs, impact on military, and impact on the population.
From history: use of the military to occupy and police the population of the US colonies by the English Crown led to increasing violence, resulting in such events as the Boston Massacre (soldiers killing protestors) and the Gaspee Affair (citizens torching British ship).
From earlier history: after the first English Civil War, the military directly ruled England through 10 Major Generals, to what was, by everyone's assessment, complete disaster and contributed to support for bringing back a monarch.
From other countries' histories: use of military to perform police functions has increased around the world in recent decades, and with it increased violence and human rights violations (torture, sexual violence), and have undermined efforts to reform police. (
https://t.co/lRbevMdOqj)
As for pragmatic needs: the strategies, recruitment, staffing, structure, systems, resources, and value systems of the military and the police differ, for good reasons. They are designed to accomplish different goals.
Just as the police would perform poorly against even a moderately effective invading force, the military will perform poorly (at least over time) at police tasks. Effective policing aims to enlist the citizenry as an ally; militaries aim to crush their opposition.
The mismatch of military and policing is part of the reason that long-term occupations -- such as in Vietnam, Afghanistan, and Iraq -- have largely failed, and have required devolvement of policing to local populations and governments to become even marginally effective.
The use of quasi-military police, by contrast, has not reduced crime over time, other than of the most visible and least socially troubling sorts. Rather than reducing, it increases organized resistance to all aspects of civilian government.
In a policing environment, protection of third parties is a priority -- there is no sense in shooting bystanders (even accidentally) to prevent a property theft or even a single physical assault -- the life/harm tradeoff is not worth it.
In war, we often (with some discomfort and controversy) inflict bystander harm, when bombings, artillery, and long-range weapons are used. True, technology can reduce third party harms, but they persist, and are often viewed as necessary, given the risks of war.
Police are trained to routinely interact with witnesses, to collect evidence, to prepare for trial. Their jobs are only partly done when an arrest is made. Soldiers do not receive such training, typically, and do not have systems to track and maintain evidence.
(Obviously, there are military police who are the exceptions to the prior tweet, but the use of military police per se is not primarily the focus of current controversy in the US, but instead it is the use of the military in general.)
Importantly, too, though harder to prove, the value systems -- the culture -- of police and militaries properly differ, at least in emphasis. Military values include an emphasis on those that aim at victory: loyalty, valor, duty, honor, courage.
Police value systems are often unstated, but implicitly include grounding in authority from law, close relationships with communities, and speedy responsiveness to calls for aid.
The police and military do share values. They both value self-sacrifice and public service, and they both include elements of respect for others in their value training. But the differences in emphasis are real.
The military does not train to quickly respond to individual citizens' need for help -- they view their public service as serving the more abstract goal of national security.
The military does not train soldiers to view every one they meet as a likely witness and direct beneficiary of their services, as opposed to being a potential enemy combatant in disguise.
Finally, mixing military and police roles will undermine the effectiveness of both.
Failure by the military caused by giving it police tasks for which it is not designed leads to demoralization, which impedes recruitment and unit cohesion, and can even undermine the most basic military norms, such as following commands.
Use of the military diverts resources from the police, and diffuses responsibility for misconduct or failures to respond to requests for help. It confuses lines of authority and over time increases inter-agent conflict.
Bottom line: there are good reasons that by law use of the military is restricted heavily in the US, to situations that reduce to armed rebellion, refusal by states to comply with federal law, and complete breakdown of the court system.
Only when local authorities ask for help, or when local authorities -- after a proclamation warning them -- fail to restore order, should the military be used, and then only temporarily and for distinct and specific purposes.
All of this may be so basic that people have forgotten it. Time to remember why the Joint Chiefs of Staff don't want to do the work of the DCPD.
Addendum:
This thread is not meant to idealize police. George Floyd's murder, and dozens of on-video moments of brutality in the last week (and before) show many police departments are in need of substantial reform. The militarization of police is a big part of the problem.
evil...prevail....men do nothing ) 
