There is no money in the Federation.
Housing is provided.
Planets are provided, if the Trogs want their own planet, or they can live anywhere where there is room.
Transit is provided.
This is a lot of passive voice. We aren't told
who does the providing and what motivates them to produce. I know there are countless interesting ideas that we should probably save for another thread. For this discussion, we can take at face value the claim from TNG that human social problems have been solved, and they were probably close to solved by the age of TOS.
When I imagine such a utopian society, I imagine there still being people who struggle. People raised in a mine where there is gas that causes mental disability are a perfect example. I imagine they didn't get the same treatment as children as people with parents with professional jobs on earth. So they grow up to be different people. Some get out of it, but some repeat the behaviors of their parents, even if they are removed from exposure to the gas.
I think of Ensign Ro as an example. She visits that camp of Bajoran refugees and says they reminded her of her childhood. She got out of that life and wants nothing to do with it now. Despite being out of it, she still has a different attitude from people who group up in prosperous conditions.
Maybe it's my own limited vision because I consider these social problems to be a fact of life. Maybe to a reader from TNG times, my view would read like someone in antiquity saying city-states being at war most of the time with the victors murdering or enslaving the defeated is just a fact of human life. I imagine in some perfect world where we can snap our fingers and get as much food, transportation, housing, etc as one person can practically use, there would still be people struggling. In my head-canon, this is how the Troglytes live. The UFP has amazing technology to produce things for pennies that aren't worth accounting for. It has evidence-based social programs that help troubled people before they turn to crime or end up in poverty and do it in a way that respects individual rights. And despite those amazing achievements, there're a bunch of Troglytes who speak a variant language that the UT can't always translate right, whose parents smacked when they got frustrated with their own lives, and who don't have the tools to understand how the galaxy works. They can't read Ardanan fluently. They don't know math, so they can't understand concepts like solving for an unknown variable. They don't know logical fallacies. Folklore about demons and weird conspiracy theories sound plausible to them. They have a vague sense that their struggles are someone else's fault or that maybe they really are losers.
When Kirk sees all this, he says the Federation Bureau of Industrialization can help solve these problems. It's possible Kirk is somewhat overstating how effective Federation institutions are at solving problems like this, but I generally think Kirk is an honest person telling the truth. Vanna is rightly skeptical. She says the Ardanan gov't said this centuries ago, and the problems were never solved. In my head-canon, they are both right.
Federation institutions can solve social problems on Ardana, but Vanna is right that social change will be slow in coming. Providing for the Troglytes' material needs is not enough to solve their problems overnight.