You need to understand the difference between "Net Worth" and "Personal Wealth".
Let's say Paul Allen wanted to build a new arena here in Portland. Last I checked, his net worth was around $4 Billion. But that worth is in the stocks and bonds of properties and companies that he has stake in; as well as numerous deals and contracts. That isn't just cash that he can throw around and spend at his discretion however he wants.
If he absolutely HAD to, he could probably sell off much of his stock and raise a few hundred million dollars. But that is hardly enough for a stadium of any credence.
His actual WEALTH, that is...his actual money that he has to spend in his various bank accounts and Trusts....is probably somewhere in the $100 Million range....perhaps $500 Million at the most.
I know how much we would all like to think that Billionaires can just build and own whatever they want on their own dime. And yes, it's true that they are able to do a LOT with the fortune that they have.
But self funding a stadium out of their own pockets? Nope. There's a reason why it's usually a corporate-sponsored task (building and running a stadium), and not one of individuality.