The fact that opportunity is driven largely by networks, and that networks are typically class-gated (not exactly wealth-gated; most people recognize that class and temporary circumstances aren't the same thing.)
Unfortunately, social seeking by the poor who aren't mentored on social signalling by someone already in or experienced with higher classes is likely to reflect lower-class misconceptions of higher-class signals, and fail as class signalling.
This is true, but what kind of opportunities are of vital importance for someone who is wealthy already and which of those can't they just buy into without networking? Or, to put it more plainly, you've got a nice house, your kids go to the best schools, your capital income provides you with a comfortable lifestyle, what "opportunities" are you lacking exactly?
What's so interesting in the rich (and supposedly educated, I'll take your word for it...) groups that you have to buy into them with expensive junk?
Do you have any idea how many uneducated rich fools there are nowadays and how they spend their wealth in just as stupid ways as the poor, the only difference being that their capital income often actually sustains that foolishness? LVMH's success is a good hint.