Interesting. Does rich sound like a balanced person? Systemically, any positive deviation occurs at the expense of some other value.
In other words, no such thing as a free lunch.
Being rich means being better in one (or a few) areas, and proportionatelly sucking at another (one or few).

Does bragging about being rich actually means (unknowingly) expressing own incompetencies in some other (potentially more important) area of life?

There’s live example: An acquaintance is a very (a bit too) proud owner and a leader of his company. He likes to express that often. But he apparently sucks at leading his own family. His wife and kids have left him, because they have no life with him (giving his whole life for the company).