"why do influencers always film in public"
Those are the obnoxious ones who go out of their way to make their content everyone else's problem. You know the ones -- and yeah, they exist everywhere, and no one likes them.
But this filming in a car thing is very uniquely American -- you rarely, if ever, see people from other parts of the world doing this, even if they're making the exact same kind of content. The majority of content filmed inside a vehicle by someone not from North America is when being in or around the vehicle is integral to the content being made (like a car review.)
To stick with this example, food reviewers can and do make their reviews right there in the restaurant -- like I said, it's not exactly difficult to set up your phone or compact camera and talk at a reasonable tone and volume so none of the other people around you are disturbed, aside from the occasional sourpuss who might give you the stinkeye regardless, and still get excellent content. My partner often does this kind of thing and not once have we ever felt the need to sit in her car to do it.
I don't have the slightest problem with people eating and filming in their cars -- the reason this post is here is because of the way Americans, and uniquely Americans (and Canadians, I guess) have been systemically primed into viewing their massive, cavernous cars as a viable third space to do this sort of thing when the rest of the world doesn't, because there's plenty of space outside to do it -- and even when there is space to do it, they gravitate back to their cars because carbrain.