Had you thought of this back in 1937, and written a paper about it, you might have won the Nobel Prize.
Air pollution is what economists refer to as a negative externality - along with overfishing, noise/light pollution, congestion on the roads, etc. Basically, externalities result when people do not have to face the full cost of their actions - a polluter does not have for the damage his pollution does to others, a driver on the highway does not have to pay for the delay he causes for others, etc.
In economics, the Coase Theorem says that in the absence of transaction costs, allocation of property rights will resolve externalities efficiently, regardless of how those property rights are initially allocated (because people will bargain for them). Economic efficiency means, basically, “for the lowest possible total cost to society”.
So, according to that theorem, letting Donald Trump own the air would be an efficient solution to air pollution, global warming, and what have you. The effect would be the same as letting me own the air - or distributing ownership of the air individually among all citizens in the US (i.e. each citizen is given the right to emit 1 ton of CO2, 2 tons of SO2, 5 tons of particulates, etc.). The critical factor here is that people are able to buy and sell these rights: how they are distributed initially does not affect the cost to society.
Giving all rights to Donald Trump would make him even richer - but from the standpoint of economic efficiency, that is irrelevant. The cost to society would still be minimized, regardless of whether Donald Trump becomes a lot richer, I become a lot richer, or everyone becomes a little richer.
Why doesn’t anyone do this? Well, there are three arguments against it: first, the theorem only holds if transaction costs are insigificant, and one could argue that they would not be. Additionally, one could argue that enforcement of property rights to the air would be difficult. And finally, realistically, determining how to fairly distribute air pollution property rights initially would be difficult.
Personally, I don’t think these problems are insurmountable. In general, economic theory gives us a way out of basically every social and environmental problem we have. But politicians (and people in general) are idiots who don’t understand economics.