The problem is that there are no truly 'public' interests, there are only clusters of private interests. Going down this route would eliminate all non-profits (which I'm not entirely against).
And other people claim that the personal is political and that there are no truly private interests.
In practice, there is a shared understanding what acting in the public interest means in that particular society. Laws can also provide a non-exhaustive list of examples to clarify the meaning.
I disagree that there is a 'shared understanding'; for instance, the latest Freakonomics podcast episode featured an interview where the subject stated that live theatre was a social good that was critical to a functioning society, and worthy of public subsidy. I like theatre, but think it's a luxury good. There are many similar 'interests'.
It obviously depends on the society. Theatres run or subsidized by a state or a city are common. In many countries, supporting national culture is seen as one of the key functions of the government. Most people in those countries agree with that, and even those who don't generally understand that they are in the minority.
Now we have to argue about "culture". I'd say, movies and net series are culture and well funded and popular with the public. No need for subsidies for unpopular "theater". Also, according to that same episode of freakonomics, average income for theater goes is $270k a year. Those fans can afford to pay for their preferred entertainment. The government does not need to subsides them.
What's the median? The median excluding NYC, LA, and SF? Why is freakonomics using average? They know that's a 'manipulate public discourse' number not really a useful one, especially for something that can easily have 1 or 2 9 to 10 figure net wealth individuals in attendance.
Public subsidies to movies are common, especially in countries that are not very popular in the international market. TV channels and streaming services are often required to have a certain amount of domestic content. Even video games get public subsidies.
What you say about the average income of theater audience sounds very foreign to me. I guess that elitist theater is the only form that remains viable when it has to rely on the market and charitable donations.
When I was a kid, theater was something you went to on a school excursion every year or so. It wasn't my thing, but some of my friends got interested in it. Later in the university, our student union had a semi-professional theater group that had become a national institution. Many student organizations had hobbyist theater groups. Even students of science started one shortly after I graduated. And before my time, socialist theater used to be a big thing. But that was when socialism meant actual socialism and primarily appealed to the working class.
> In practice, there is a shared understanding what acting in the public interest means in that particular society
No there isn't lol. Half of society thinks promoting one political party is in the public interest, the other half thinks promoting the other one is. Same for religions, same for handling unwanted pregnancies, same for education...
Promoting a political position or a religious belief usually counts as a public interest, as that's at the core of freedom of speech and religious freedom. I've never heard anyone claiming seriously that their political party should be a tax-exempt non-profit, while the opposing party should be a for-profit corporation that has to pay taxes.