>the benefits of the business goes to the private person
It's not 0 sum. Someone else, potentially from the community, also gets value in exchange.
It's not 0 sum. Someone else, potentially from the community, also gets value in exchange.
A business profiting off making goods/services for a community is good and all, but can still produce externalities, for which everyone, including those who _didnt_ participate in the business transactions, would pay.
There are zero private businesses which generate positive externalities that they do not charge money for (and if they did, then it's no longer an externality). To do so would mean they leave money on the table! They can only shed negative externalities.
Generally it means that they can't capture the full value they add.
If I have a business installing domestic solar panels, I can capture the economic benefit to a homeowner of getting cheaper electricity, but not the broader impact of helping to decarbonise the grid.
(There might be a subsidy for this business where you live, but that's irrelevant: in principle a business like this can exist and be profitable without capturing all of the value it creates).
A trade takes place when both buyer and seller feels they gain something from the transaction. In general neither side captures all the surplus value, if they did the trade would not happen.