Sure, but is that a Utopia? He doesn't have everything he needs if he's longing for a partner, does he? And why does he want one? Prestige? Approval? Companionship? All of those things suggest that his needs are not met. If there are humans in a utopia - it's not a utopia. Someone is always going to covet something someone else has and fuck it up for everyone.It could be written as a slice of life type story. I can imagine many ways to make it somewhat exciting. Everything doesn't have to be about death and explosions all the time.
How about something like this:
Markise is attending the utopian world faire, he wants to find a partner for a great dance among all the women of the city. Can he find the right partner in time? Follow Markise in a world of richness and splendour as he meets all sorts of unique women and try to date them in the backdrop of floating sky palaces and self-driving flying taxis.
The above becomes a story of if he can find the right partner for the dance in the right time. As the story progresses we meet many strange and even eccentric women and characters who have their live's needs fulfilled and who focus on their own character development as well as some strange or unique hobbies/interests. One such hobby could be to collect stones from all the highest mountain tops in the galaxy, and what they may have seen.
Of course things don't always have to be about death and explosions (pretty big jump from utopias are boring), but conflict is what drives a story. Even in slice of life, there is something they need to do, get to, something. Even if it's just going to the store to get toothpaste. Even if it's just emotional or growth related, there's still something more.