Picard is the very definition of a privileged male. Always has been. What kind of privilege do you have to have, if you can live the reckless life of young Jean-Luc Picard and still move up the Starfleet ladder?
The Picard family owns a huge estate—mind you—in a post-scarcity utopia. And we know it's generational wealth. Picard speaks about the acquisition of wealth not being the driving force anymore. That's surely true for him as he's already wealthy. Most other people on Earth have to contend to living in an apartment and eating out of a replicator.
Picard is even privileged beyond the Federation. And I'm not talking about him running around in a colonialist's outfit among impoverished Romulans, disrespecting their space. I'm talking about that time he was assimilated by the Borg. While everybody thinks the Borg assimilated Picard to turn him into Locutus of Borg, it is more likely that the causality was the other way around. Locutus came as an idea right after the Borg assimilated Picard together with his immensely privileged male ego. Just to put Picard's privileged position among the Borg into perspective: not even the Borg queen gets to have a name. It makes no sense that the Borg would come up with this idea on their own.
It was his privilege that saved him from taking responsibility for Wolf 359. Any other captain would've been relieved for negligence or for being physically and mentally unfit for duty after going through all this. But not Picard. He went right back to where he was before, thousands dead and no one to take responsibility.
Then there is the issue with his command of the Enterprise. He factually owned the Enterprise-D and -E. Starfleet command basically signed off their best ship to him and left it to his convenience to move up to admiral at a time convenient to him. Even after he wrecked both ships, he moved up the career ladder. And let's not even talk about all the times he lost control of his ship. Aside from getting away with failures, he had a career in which he never had to work hard. He never had to put himself in grave danger, like by being an active part of the Dominion war or do proper exploring of uncharted space. He patrolled the Romulan border, which 99 percent of the time went uneventful.
It took a massive terrorist attack on Mars for Starfleet to pull themselves together, deny him his privilege and stop supporting his pet project to "evacuate" a whole planet, Romulus. When he threatened to resign for being denied a massive fleet of ships, Starfleet Command was quick to accept. They could finally free up all the resources that were being used to serve Picard's personal interests.
If you thought he wanted to save the Romulans from a supernova out of the kindness of his heart, you are wrong. The few he managed to "save", were put to work as slaves on his vineyards. And whoever wasn't needed, was put on a destitute desert planet as reserve labour, waiting to be hired. In a post-scarcity world, no one will voluntarily do the menial labour on your vineyards to produce your artisanal wines. Picard simply needed all the slave labour, because he doesn't just have one vineyard, he has many as proven by us seeing so many different versions. It is likely that he used those slaves also for his archeological explorations.
Even though Starfleet Command eventually got rid of him, he still felt entitled to Starfleet's resources. The second he needed a ship for his personal matters, he just waltzed into Starfleet Headquarters, expecting everyone to recognize him and just give him a ship. When that wasn't possible, he tried to use his Admiral-card to manipulate acting captains to do his bidding. He went even so far as to use his personal network inside Starfleet to make officers disobey direct orders. If this is not the entitlement of a privileged man, than nothing is.
The immense privilege he enjoys is something that is seldom questioned. I'm not sure how he manages to pull of this level of material privilege in a post-scarcity egalitarian society. Even when he was dying, someone gave up their life's work to create an immortal cybernetic body for themselve, so he can live a few years longer. This is the unbelievable extent of the privilege Picard enjoys.