But even on the public side: yes, this would be entirely appropriate. It's not clear what the alternative would even be; what would it look like to have civilian evidence in e.g. traffic accidents if people weren't allowed to take pictures of others' cars?
2. In such a case you have a need to know that supersedes one's right of privacy. Are you saying you have a need to know where Elon Musk is at all times?
I don't have any particular need (or interest) in knowing where Elon Musk is. I also don't know where he is at all times with the information in this flight tracker: I only know the parts that are already necessarily public.
Law is fundamentally casuistical in nature: there are standards that apply to John Q. Publics (like you and me), and there are other standards that apply to the Barbara Streisands (and Elon Musks) of the world.
Put another way: the courts have overwhelmingly recognized the rights of "paparazzi": if you're a public figure, there is going to be independent public interest in your life.
The interest can't be intrusive (meaning that it doesn't enable someone to break into your house and take pictures of your underwear drawer), but it does allow citizens to use any public information available to them. Since airplane information is public by necessity, there is no reasonable legal structure that enhances Musk's privacy without compromising well-trodden expression rights.