These aristocrats do not have any political power, but they have considerable social and economic privileges. Many of these families still own considerable land and along with it, tax advantages and certain rights that are attached to the land. Within society, they enjoy considerable deference. If they want something, they frequently get it. The have very important connections, an elite education, and they can use their title to find the right job, or the right investment opportunities. They can fall into things that you will never know about. Their titles no longer come with legal privileges, but those titles still count, in Europe these people still punch about their weight class.
What most people do not realize is that there is a class system still in most European continental countries.
For example, my father in law worked for a company founded by a former Swiss national. They sold and serviced imported high end European textile manufacturing equipment into the US primarily. He had tried to start his company in Switzerland. However, because he did not come from the upper class he could not get a business loan from any of the Swiss banks. He moved to the US and started the company here.
This company made him rich. It employed many people including my father in law who was their top salesman until he retired about 15 years ago.
People do not realize the OPPORTUNITY we have in the USA over other countries because they were born here.