You are incorrect in your assumptions, and so, although your conclusion is sorta correct it actually leads people astray from a solution.

With free energy, there is still the human who has to design and create. Even with tools to build the product at the push of a button, there is a lot of input that needs the human.

If i get my machines to plant pumpkins and you get your machine to plant melons, even with free energy, we still have a need for accounting the energies exchanged. (as your melons come in in the summer, and my pumkins in the fall... so a straight barter is not doable)

So, free energy will not eliminate money, what will do that is computer getting so good that they can actually track the exchange of goods/human energy to keep a balance of gifts.

Now, psychopaths love to be in positions of power, however, they cannot stay when exposed to light. When we expose their lies, they lose all power.

And so, we need to psychopath proof our offices of leadership. In the future we will elect people based on their compassion. (i know, weird, right?) And since psychopaths can only imitate compassion, they will lose.

Free energy devices will only come into existence after we will never use them for war.
So, that will be after we get all the psychopaths out of office and stop believing their lies, and learning to live with each other peacefully.

So, the free energy will not eliminate the power structures, the elimination of the power structures will bring free energy.