I have a lot of reservations about this. An armed citizen, with the proper training and weapon proficiency, could be a help in some cases. But I have also seen situations that were escalated by the armed citizen who really should not have gotten involved, or at the very least, should not have brought a weapon into the situation. It may be somebody's "Second Amendment Right" but that does not mean that a weapon should be injected in a situation that does not call for it.
There is also the potential for harm to the armed citizen if he or she is not known to the officer(s) responding, especially if they do not follow the commands an officer or deputy gives them. How many times have we arrived at a situation and found out that our supposed victim is actually the suspect or has a warrant on file? There's also the issue of liability for the agency/jurisdiction if citizen involvement is encouraged and then the encounter goes south when the citizen actually tries to step in. That may not be an issue for elected sheriffs, but for appointed police chiefs or other agency heads, it would be a major issue to confront. In some cases, that issue alone would make any training by the agency impossible, for all practical purposes.
Each jurisdiction and situation is different, so I think it's important that we not make any blanket statements or assertions about this or similar issues. This may be the way to go for some, especially those that have a lot of territory to cover with inadequate manpower. But it's not nearly as simple as it seems.
Stay safe, everyone!