In the US, The police are so empowered and do it all the time. I am unsure why gp thinks otherwise. They are not required to nor do they simply get arrest warrants in every case they think they have probable cause. Anything else would be silly. They would get an arrest warrant, arrest, it would get dismissed without charges at the initial hearing a day later.
If the DA is involved already or they know the office policy, Cops will not get an arrest warrant if the DA is not going to back them.
If DA is not yet involved they may do it for various reasons, but again, they usually aren't going to touch it if they know the DA won't back them. They have too much to do to be that passive aggressive.
As for the other part, Whether individuals can get arrest warrants actually varies from state to state, though it is very uncommon no matter what.
(It's worth noting that Boudin was recalled nearly a year ago, and so perhaps the SFPD will have discovered the will to cooperate with the new DA.)