Aristocracy is different from this. Generally, aristocracy is both hereditary and disconnected from actual wealth.
In the UK, JK Rowling, even though she is richer than the Queen, is not an aristocrat. She is, in fact, upper middle class. Someone who's born into the aristocracy, even if they're not especially wealthy, is an aristocrat.
You're just noticing the difference between a 1000 year old aristocracy and a burgeoning one.
Aristocracy always begins with a way to define the elite. Over time social mobility will decline and people will start to notice that it's mainly the children of elite who become elite. Eventually this will lead to the belief that only the children of elite can be elite. Once this belief is entrenched, it's natural for the new reality to be codified in law.
Do remember that even in England there was social mobility. If you performed a great service for King and Country you would be granted land and title.
Social mobility exists in all societies. Just some more than others. In America we are observing the emergence of a natural aristocracy - a story as old as history itself.
I wonder if we're headed towards a hereditary aristocracy as well, because of assortative mating. People tend to marry others in the same social class; rich marry rich, smart marry smart, and highly-educated marry highly-educated. And then they tend to pass on those advantages to their children. It doesn't take all that many generations before that becomes entrenched and it becomes impossible to jump from one class to another.
People can move up or down a social class or two. I know people who came from fairly little wealth who earn decent urban-professional six-figure salaries, and people come out of families in the upper-middle professional class and become multimillionaire entrepreneurs. (Likewise, other people move down.)
Entrenched aristocracies happen when you have old money that looks down on the "nouveau riche". Every country has an old money class that considers itself more elite than the nouveau riche, of course, but they aren't really an entrenched aristocracy unless the rest of society agrees with them.
It's neither. It's just part of the aristocracy (the other part being the willingness of the rest of society to humor old money in their self-perception as being aristocratic).
I think it's held throughout history, but then again, throughout history most of the world has had some sort of aristocracy.
The historical exception is the U.S. from 1945 to 1973, as well as perhaps a few other examples (maybe Scandinavia today, or the U.S. in the early/mid 1800s?). In that time period - really, no more than a generation - we saw a big leveling of income distribution, where people born to modest families suddenly had the creature comforts that a generation before had been reserved for the aristocracy. I think most people would agree that this is a generally desirable state for a society, so it might be worth asking what was different about those time periods that made them the historical exception?
Whether it's a hereditary or mercantile aristocracy, it's still an aristocracy. A hereditary aristocracy would be worse, certainly, but that doesn't mean a mercantile aristocracy would not be very, very bad.
In the UK, JK Rowling, even though she is richer than the Queen, is not an aristocrat. She is, in fact, upper middle class. Someone who's born into the aristocracy, even if they're not especially wealthy, is an aristocrat.