Depending on the circumstances, absolutely. Assuming that serious unjustified injury or death would occur if they failed to act, there should be some legal window in which they’re allowed to prevent the harm. Private companies (and individuals) should not be required to stand by helplessly while people are hurt.

Indeed, legally, private individuals and companies are allowed to act in emergencies. For example, I generally should not break into my neighbor’s home. However, I am legally allowed (and morally obligated) to forcibly enter their residence if their house is on fire, or they’re being attacked by a burglar, etc. and I am able to prevent some of the harm.

Of course, if we assume we’re talking about situations where the government needs a warrant, the legality becomes more complicated. At what point does something become an emergency? I would say it’s not an emergency if there is time to inform the government and to let the government prevent the injury. If we assume the government is unwilling or unable to act, then the window for action should expand by some measure.

You mean something like citizen's arrest?

https://en.m.wikipedia.org/wiki/Citizen%27s_arrest

Exactly. Indeed, in Phoenix v State, 455 So.2d 1024, the Florida Supreme Court implies that a private citizen could request and receive a warrant to arrest a felon. They say the citizen could be excused for failing to obtain a warrant by proving the person arrested was actually guilty.

This is obviously a bad idea, private companies or individuals having the power to arrest people because they want to? Look at the recent few years of history in the US where multiple experienced and distinguished (at least by resume), members of the us govt, senators, reps, tried to subvert an elections, dozens of lawyers told them it was illegal, we have their email and texts telling them. That group still acted to do many illegal actions, lie about it, tried to cover it up. And they still deny any problems with their behavior and choices.

Private companies having arrest rights is just a nonstarter of an idea (putting it kindly).

If all of these government officials did something so terrible, wouldn’t that suggest that the government should be denied the power to arrest people?

I’m not suggesting that private individuals authority to should be expanded to allow for arrests, after reading many statutes and caselaw, it appears that there are many circumstances were private companies already do have that power, even if they do not exercise it very frequently.

Private companies aren't, but in certain circumstances private citizens working for those companies are. In the US (except perhaps Georgia?) if a crazy guy comes into your workplace waving a knife around, you're allowed to disarm him and pin him down on the ground.

https://en.wikipedia.org/wiki/Citizen%27s_arrest#United_Stat...