So far not mentioned in replies to this is that there are many examples of productive organizations that do not organize around money. Two leap to mind:

• Military. Rarely do the various units and platoons trade with the other components of the military for their supplies, nor do they bid on missions. To the extent trade occurs it is usually barter and usually outside official accepted ways of doing things.

• Business units. Large businesses may use separate calculations of returns to determine some very macro choices between business units.

But there is essentially always some size of organization below which the subunits or individuals are not trading using money to get things done. Marketers don't bid to engineers to get the products they think they can sell. Engineers don't bid on the projects they want to work on within the organization.

Indeed the fact that firms form to avoid a whole bunch of bilateral trading is analyzed by one of the most respected economists ever Ronald Coase on the Nature of the Firm.

So another version of the answer to the OP would be that the reason EVERYONE on the planet doesn't do it is because the coordination problem without money and trade is too hard (meaning you will get a vastly suboptimal result) to do on a global scale, but it works on smaller scales. So whatever it is you want to achieve, form an organization to solve it, give them a pile of money to trade with the rest of the world, and do not require them to organize internally on a trade/money basis. If you make the organization too big, it will either organize internally using trade or it will be very ineffectual.