The best explanations that can be provided are:
From childhood, humans are indoctrinated in leaving their homes and going somewhere else, starting from scratch, in order to do their duty towards the federation.
There may be underlying cultural biases seeing emigration as an option, but there's not the infrastructure for the kind of totalitarian education you describe.
Humans are just bored with their perfect lives and yearn to go 'into the wilderness' for a more vital life. But why go to Deneva and not a frontier world?
Why do nearly all immigrants to (say) Canada head to the country's half-dozen largest cities, instead of the vast rural expanses? Immigrants head to places where there are economic and other opportunities. In some cases these are frontiers, although even in Earth's history frontier societies--Australia, northeastern China, Argentina, Canada--quickly urbanized. In many more cases these are "mature" developed societies which already offer plenty of opportunties. From its description, Deneva was such a society.
Even so, the enormous number of immigrants to Deneva (over 1 billion in a century) is rather silly.
It's not possible to imply that. Deneva had a total population of a bit more than a billion people. The immigrants who went to Deneva presumably had children, thus bolstering numbers a bit.
Forgive me for going into this at length, but demographics are a major interest of mine and, well, they have to be gotten right. So far I've seen little in the
Star Trek novels that contradicts what we know. The whole post-industrial/scarcity economy that the Trekverse enjoys by the 24th century would introduce new patterns.
It is worth noting that the developed countries with the highest net replacement rates are the societies that are the most gender-egalitarian and treat all their members as equals; more traditional societies don't reproduce nearly as well. I can see as a possibility the sort of sustained above-replacement fertility among humans that would provide the impetus for interstellar colonization.
That's just for humans. We have little to no idea what other species go through. We do know, from the
Terok Nor trilogy, that the Bajorans' short pregnancy--six months--made it at least possible for Bajorans to have a substantially higher rate of population growth than what the Cardassians considered seemly. Maybe that explains why Bajorans are so visually prominent.
The question of the demographics of Vulcan and Romulan populations, with their very extended lifespans but postponed family formation, is likewise interesting. What schedule do they bear children at? Is the main difference between Vulcans and Romulans a tendency among Romulans to form families on less constrained schedules, perhaps boosting their fertility?
Et cetera.