The short answer is absolutely not! No proof of a concept will ever change the ordering of this world. No logical argument will ever make all the depersonalized or self-interested forces and organizations in this world cease their activity, even when it is brutal. No singular conceptualization of a thing will ever permeate the entire face of the earth resulting in a harmonious decision to reorder all social life. We will never arrive at a place where everyone agrees on the beauty of an idea and then decides to put it into action. That is the stuff of utopias.
Critiques of money and how it realigns social relations are enormously plentiful. I first encountered these arguments in the marxist and anarchist worlds among situationist writings (Guy Debord) and egoists writings (Wolfi Landstreicher) respectively. The concern that numerous continental philosophers (e.g. Gilles Deleuze) pay to exploring notions of qualitative vs. quantitative thought and conceptualizations is an attempt to address and challenge the deadening, mechanical, capitalistic, identitarian and reductionist effects that economic or quantitative thought produces. It is not for the absence of these ideas that money continues to distort life and the world, it is because ideas apply no force in the world simply by being known. All your pretty thoughts will crumble when the force of the state or capital successfully put you in their cross-hairs.
Even among status quo oriented economists or governmental bodies the notion that money affects the world (you said "distorts reality") is entirely common. Enormous effort and coercion is applied to exactly these aims. There are government bodies the world over tasked with exactly this endeavor.
You keep coming back to the notion that it is merely a matter of ideas: misinformation enslaves us; through logic we could break our domination; what if we examined what money does. This seems entirely naive. This type of thinking seems to cover a desire for some utopian transition away from capitalism that entails no struggle or conflict except in the realm of ideas (where yours are prefigured to win - as per the phrasing of your question). Moral suasion has never had and will never have a chance against well structured, systematized, and bureaucratized power. This conceptualization of the way systems and forces order and affect the world seems never to address the messy, divergent and violent world I live in. It seems like fantasy to me.
Additionally, you use "we" and "humanity" in really presumptuous ways and you use "well-being" as a magic code word which makes me highly skeptical of the proximity of our desires or dreams. Your use of "we" is suspicious and does not include me or the people I know in any meaningful way. Your thoughtless use of "humanity" as something that totalizes everyone's needs and coordinates our interests into one single set brings me to the cusp of revulsion, as does the way this abstraction becomes a force that impels me to action along the lines you desire (this universal "well-being" and the actions that must be taken to ensure it).
