To set aside the feasibility of such a space age, I evaluate it from a different perspective. Which is why I see a fundamental flaw in your conception of it. But I am in no way judging you negatively for this, I would like to emphasize that. Since we learned to respect each other, such debates are much easier to have.
Let's assume that it happens as you say. That once humans have overcome the teething troubles and the loss of human life, they will be able to construct such fantastic ships and make them suitable for space. What would that change about the human mentality? Why should the space age change what causes conflict on earthly territory? Hear me out to the end.
As I see it, humans would carry their existing potential for conflict into space. What man is not able to solve here, man will not solve when he has detached himself from here. Where he fights for resources on earth, he will also do so in space.
From my point of view, the infinity of space leads to the misconception that this goes hand in hand with the infinite utilization of celestial bodies. And that prospecting for valuable resources in our solar system would be a joint cooperative act by the passengers. Which maybe means that it would have to be a single ship so as not to jeopardize the fundamental cooperative spirit.
But where you already have a ship with the quality of life you describe, it can be assumed that in the run-up to this gigantic process not only terrestrial matter has already been exploited for this purpose, but also extraterrestrial matter (such as the asteroids you mentioned). All of this actually requires a very determined cooperation of all people, not just a part of humanity, as I see it. Here, I imagine huge problems.
But let's assume that everything succeeds, that any conflict that arises before and during this project is overcome.
Nevertheless, I am convinced that not all people would be destined for happiness and a perfect existence. I don't assume that you yourself dream of it being perfect in all respects.
People, because they are people, would continue to harm and kill each other. Space existence would not free them from expressing their hostile nature (next to their friendly one). Nevertheless, the infinite nature of space would not hide the fact that every space - even the galaxy - will always be subject to limitations. Namely a technical and distance-related one. So what a ship urgently needs may be available in abundance out there and yet whatever happens will happen: That the technical factor - or others - gets in the way.
So you can have detected a planet of gold on your long-range sensor and yet the distance is too great and your ship is not sophisticated enough to reach it in time and that is the limit to absolute freedom that I mentioned at the beginning.
There would be discussions on this ship, some would say it's no use, you have to think of alternatives, others would be angry about it and want to try it at all costs and ultimately you would have this conflict on board, like countless others - people would be harmed and murdered. To think that jumping into the universe would remove the limitations of freedom experienced on earth is a misjudgement in my eyes. It is a beautiful thought, no doubt.
You may think that at least man would not blow up the very mothership he lives in, but I would argue that it would not be only one ship but several (giving the highly advanced tech). Or, you breed disturbed souls that act on self sabotage etc. - man does not escape conflict, otherwise he would be a total other creature.
So, I think that my premise
"Every circumstance you find yourself in, comes with certain limitations and restrictions, without exception..."
still stands. Why shall it not? You need not to eliminate it, because firstly, you can't and secondly, that is life. You win, you lose. You live, you die. If you're lucky, the main part of your life granted you joy. But in every lifetime there comes the situation to face its tough nature.
Nevertheless, I would like to conclude by saying that your dream is certainly also that of other people and that I would not actively oppose it per se, because such projects cannot be prevented by their very nature. There will always be pioneers and visionaries. Along the way, they will inspire many people and make them happy and just as many desperate and unhappy.