The Federation is the ultimate socialist expression. Why WOULDNT they build it there?
Not necessarily. The Federation might also be viewed as the ultimate expression of the free market, which results in the end of the market.
It is not difficult to look around us and see that technology is continuing to improve productivity. Well, what is productivity? It's the ratio between wealth (stuff) produced and the human input required to produce it.
Improve productivity indefinitely and what eventually happens? A LOT of stuff is produced with very little input by humans.
In such a society there would be no demand, in the economic sense, for the services most people are capable of contributing. Just as at present the market for galley slaves is non-existent, it is likely in 20 years that the millions of people presently employed partially or exclusively as vehicle drivers will be obsolete.
Extrapolate these trends indefinitely, and eventually a majority of the population is just superfluous to the operation of the economy. Still great demand for those capable of continuing to expand and improve on technology, but those people are by definition those WAY over on the right side of the IQ bell curve. There just aren't very many of them.
This society would be incredibly productive of "stuff," but what do we do with all those people for whom there just is no economic demand?
At some point, doesn't such a society start to converge with that posited in Star Trek?
The market is by definition a method of efficiently allocating scarce resources. It fails, or possibly just reaches its culmination, depending on your POV, when resources aren't scarce anymore. In the world of Star Trek the only scarce resource is the minds of those few capable of continuing to improve the productivity of the system.
And one can make a case that computers and software will eventually improve to the point where even this resource becomes non-scarce. At which point all humans are economically redundant.