I'd argue that inequality is still present on Earth. Look at the property that Picard owns. Check out the property that Kirk owned in Generations. And we can see the quarters that Chief O'Brien had in DS9 versus the others. There are the haves and have nots. But now you have space travel too. How many people could afford to get off planet to pursue opportunities? The TV series Picard makes this more clear than TNG ever did. In Picard it seems like the Federation is imploding, and that would create a lot of opportunities.
As for con artists in the episodes, how many would you consider successful? Can you point me to specific episodes, where there are legit cons going on that succeed? I'd love to rewatch them.
Picard's property was passed down for generations, so I don't really see an issue there.
Regarding O'Brien's quarters on DS9, keep in mind he had a wife and daughter and later a baby boy, so it makes sense that a married couple with kids would get larger quarters.
Regarding Kirk's cabin in GENERATIONS and his place in ST II and III, I really don't know. The cabin might have been something his brother or parents had and he moved into it later, and his place in II and III might be typical for an Admiral.
On the topic of the post-scarcity, no money in the Federation (at the very least, Earth), I think STAR TREK could take a page from THE ORVILLE on how they explained it. Basically, reputation is your currency. All needs... food, shelter, education, etc... are all met, and you can do whatever you want, as long as you aren't being lazy. Doing absolutely nothing gets frowned upon, but you have freedom to do whatever else... study, be a musician, join the fleet, be a researcher, and endless other possibilities.
I like to think that's what goes on in the Federation, too. At least, with humans and Earth.