Men will still compete for the sexiest women (of which there will still be a limited supply). Women will still compete for the sexiest men (of which there will still be a limited supply).
And as always, people will compete for luxury items. We do see on Star Trek that people don't simply get everything they want. You want to be captain of a starship? Do you just replicate one for free?
We could talk the same way about money and greed, which seems your concern. The capitalist myth about the origin of money has done a lot of damage; in most "primitive" cultures, we don't tend to observe people bargaining in barter systems... instead, they tend to be built on elaborate systems of gift-giving and indebtedness. The natural human proclivity in many cultures has been to aid neighbors when needed, because the assumption in primitive societies is that "we all need to stick together," since otherwise you'll likely die of starvation or by wild animals or by neighboring tribes or whatever.
Are you talking about people within a single clan/village, or people within a large federation of villages? While a small communist society is certainly do-able, especially when everyone is pretty closely related, the willingness to sacrifice one's own desires for the good of the group tends to drop off pretty quickly when people are being asked to sacrifice for strangers and especially for strangers who are different.
I think pretty much every nuclear family is best run as a communist dictatorship (with two power-sharing dictators). But the solution doesn't scale easily.
You are begging the question there. Is it really human nature to want to amass personal wealth?
It is human nature to want to amass the resources to help you get laid and help your offspring do the same. This means not just wealth but also power.
Even today, many people have moved past that and prefer to be comfortable and happy rather than miserable but with a pile of gold. Anyway, the Federation offers citizens something much better than personal wealth, which isn't even that meaningful when poverty was eliminated long ago and replicators/holodecks can cater to almost every desire and whim. The Federation offers people the chance to do what they want, with the amount of commitment they want. If my needs were more than catered for and I could work on whatever I wanted to, I wouldn't care about wealth.
Even if everyone has enough wealth to live comfortably, guys are going to struggle to get more wealth so they can impress the girls. If you live in a town where few guys have a care, you can be hot stuff owning an old Honda Civic. But if every guy has one then you'll want a Lexus or a Camero to make you hotter. Even in Star Trek there is not an infinit supply of women.
A large happy prosperous communist society?
Well, most of the best places to live in the world are socialist. Sweden and other northern European countries are very far to the left of the US and yet have a better quality of life, less poverty and more happiness. It seems to be the way the human race is heading as most societies become more socialist as they develop.
The good old few mono-ethnic examples made up of small norther European countries - quite the opposite of the Federation which is multi-ethnic, multi-species and huge.
Better than the US.
Not at the moment. But if we keep electing people like Obama and Trump/Hillary, it won't be long.
I'll call and raise you...
"Two of the major problems that bison face today are the genetic bottleneck and lack of genetic diversity that has been caused by the very small number of bison that survived their near extinction event. A third genetic problem is the entry of genes from domestic cattle into the bison population, through hybridization."
Questions? Ideas? Solutions? More bitching about it?
Breed them with nukes from space. It's the only way to be sure.
Other than that I got nothin'.
The best things in life go on sale sooner or later.