I know where you're heading, but it still doesn't work. There's more than mere fear going on, and one of the favorite leftie soapboxes is actually good proof: rich people generally wanting more money. Once you hit a certain level of wealth, there is no practical limit to what you can have, nor how much of it you can get. All without touching the principal, and there's no way to lose that core outside of gross incompetence. Basically, there is no fear nor unfulfilled want at that point. And yet, they try to acquire more money. Why? Because somewhere there's another monkey with MORE. Bigger bank account, bigger house, more cars, bigger yacht, more ski trips in the Alps, better (man)whores, whatever the measure of choice happens to be. It's an instinctive drive that goes beyond a simple fear of "not enough".
Now you're talking about two different things, though. You're talking about the natural competition instilled in us AND the drive for material wealth. Competition isn't just about material wealth or value. Setting yourself apart can be done in a myriad of ways.
If we reduce or remove the value of material things by making them universally available in whatever quantity is required for a practical purpose - beyond basic needs met - then people will find something else to be competitive about. This does depend on the assumption that we have enough natural resources available to not only meet basic needs for everyone, but also for practical purposes beyond that.
But the drive for material things really does begin at the basic stage of the fear of not having enough - the survival instinct. That's why the opposite sex finds it attractive as well, which we all know. What the opposite sex finds attractive is a pretty strong motivator. But it's a long-term process - and not something we can magically remove over the course of a few years. It will likely take generations to fully eliminate the ambition to have more than you need.
It's about security, really. You fear not having what you need mostly on an instinctual level. It's very much about something primal. Unfortunately, the human brain doesn't quite overrule the sensation of security we feel by having MORE than we need, so that we don't run out. So, essentially, we feel ever more secure the further we go beyond what we actually need.
But that's very far from the only reason people strive to get rich - but it's the origin and the primary cause. Remove that, and the rest will eventually follow.
But I don't believe we can eliminate the competitive drive, or the need for attention or love. That's something entirely dffferent. But by eliminating the pursuit of material wealth - we help ensure the even distribution of it to everyone in the world. Which is the ultimate goal.
Because many of the biggest problems in our world has to do with the differences between us (perceived or real), especially in terms of material wealth and the perception of being less because you have less.
The problem with the monetary system is that human beings are too stupid to handle a symbol of value. They can't separate value from the symbol, so they just accumulate more and more - in case something of value should become attractive, and then you need enough wealth to purchase it. The capitalistic system combined with human weakness and stupidity is a very bad cocktail. Because we're not trading things of tangible value - we're trading things of perceived value. That's why you can get people to pay 1000$ for a meal that costs 10$ to make.
There are other equally large issues to deal with, but they tend to blend together. I'd say the biggest one is general ignorance - based on denial - which is again based on the inability to ignore the instinctual and emotional drive and behave rationally. Rational behavior being, more or less exactly, that which results in the most beneficial long-term outcome for everyone.