I’m sure it would. However, I do not believe it is as easy as “people want more money.” It is all about power.
However, if we don’t have some kind of currency, we’ll have to rely on trade to get the stuff we need. Would this result in a more utopian society? I’m going to decline. Through capitalism, technology has no limitations (save for natural laws, I assume), and as a result, new innovations or ideas are always being developed to improve our daily lives. Though there are corporations/individuals that are selfish and will utilize them to make a profit, which is permissible within the confines of capitalism, this only brings me back to my initial point: greed.
Furthermore, there is a problem: while the principle of teaching something better is correct, you must identify who will help you achieve that aim. Simply stating that “the way things are now are wrong” is insufficient. There will be far too many individuals who vote against your proposals. Even if we were able to begin educating in a more effective manner, the family’s influence (and the old way of thinking) would remain incredibly powerful. For me, utopia would be a state of euphoria without end or limit, regardless of the consequences (this is my id speaking, not my rational principles). However, for another person, paradise may be the polar opposite of this—no limit or cessation of misery.
If we were to pick a middle ground, might utopia be thought as the systematic eradication of pain through a democratic process? I believe it could, but turmoil would always disrupt the democratic process. So perhaps we are living in the only utopia possible for all living creatures.