Probably, for billionaires, money is their life. If they give it away then there likely will be nothing left of them but empty husks of men. In fact, if their trust issues are justified then even their family might leave them. Giving away everything that you are is not easy at all.
Come on, lambda you're deeper than that.
Why do you think they're afraid of being left alone if they become poor ? Because once you're poor you have a bigger problem than when you're rich, and everyone knows that.
For billionaries money is their life ? Poor fools. For minimum wage or lower incomes, lack of money is their death. Who can more easily "get a life"?
Rich people can have problems, they are not invulnerable or magically wise or something, but none of their problems is being rich. The problem is being poor. And then there're other problems.
If rich people are afraid of giving away their money they have the option of giving it away or not.
If poor people are afraid of starving, or ending up in the street, they don't have any option. They feel already like empty husks of men, not potentially so. And they have the whole society pressing them to feel so.
So rich men are conditioned to believe they're only worth because of money, but the same shared cynicism conditions the poor to believe they're not worth anything at all, not even for their money.
Rich people fear that their family might leave them if they give away (or lose) their money. Poor people lose their families every day because the family is conditioned to expect richer relatives and leaves, or because they can't feed them and the familiy loses health or life, or because they end up in jail, or having to take ajob away from family or for a million things they can't control and a few they could.
Not having anything to even consider giving all, something or nothing away is not easy at all.
The problem you describe is basically some kind of low or misguided self-esteem (that's either low self-steem or high self-steam, or both?) because of a crazy value scale and appreciation of money. This is a cultural, societal, even religious problem that is not exclusive of the rich. In fact poor people suffer more of it.
Now are there worse problems than abundance or lack of money? Sure. Many. That still doesn't makes being rich a problem. Being stupid is.