Bashir's dad tried and failed constantly at a variety of careers.
Education is free, but you still need the grades and a healthy respect for the waiting lists.
The further off world you get to find a school that will take you, the further away from the heart of the Federation, the closer you get to there being money and graft that the waiting lists can be compromised.
Also I'm guessing the shittier the colony you move to the bigger the box they give you until you prove your worth, and because of the lower population there's actually opportunity to prove your worth to earn yourself an even bigger box.
Transit is free, but then again the waiting lists must be long, even if there was a colony ship in TNG Ensigns of Command that could carry a hundred thousand people, which I'm guessing is is not a ship you want to take into battle or run any races in... The Federation still boasts a population into the hundreds of trillions.
Picard has two boxes. His quarters and his ready room.
His ready room is for convince. I wonder if he has a third box which is his actual office? Thinking he probably has a fourth box too if Enterprise came with a Captain's Mess... The Captain's Yacht is his 5th box... But still Jean-Luc needed to crawl into the vents to find somewhere private to play his little pipe.
Meanwhile consider how much a Federation trained/educated person would be worth on the open market as a worker to an alien government/alien business? Cassiday Yates went into work for herself but it's not like it must not have taken a while for her her to get to that point with her own ship?