Would you rather the police be aggressive? I'm sure you wouldn't appreciate it if someone showed up at your place of work and harassed you for no good reason other than Internet clout.
And I think the activities of the police should be scrutinized heavily because they have an incredible amount of power and are accorded a very wide latitude. The police are the only people who can legally shoot you and not be tried. They can arrest you and throw you in jail. They can charge you with crimes, invade your house, and smear your reputation with the public. A police officer with a vendetta can absolutely ruin your life if not outright take it from you.
So yes, I think it should be okay for people to video the police going about their business.
The officers can't do anything about it because it's not illegal to film police officers in public while carrying out their official duties. It's a constitutionally protected activity.
Is it at times obnoxious? Sure. (Although in many cases, these videos capture police officers behaving badly, rather than live-streamers behaving badly.)
A lot of First Amendment protected activity is irritating to at least some people. Cursing at police is, in general, a First Amendment protected activity, and I don't suspect a lot of officers appreciate that, either. But the entire point of the First Amendment is to protect activity that other people might not like.