Sales would invest in RnD, and buy services from IT. HR would would need to focus on high quality services, not dictating unwanted routines.

Profit could be extracted as a tax, and all departments could be required to just break even (with an allowed buffer for investments spanning multiple years).

I've worked at such companies and it kind of sucks. Everybody optimizes for their local optima without any concern for what is good for the company. People end up a lot less willing to lend a hand to a 'rival' groups, and projects that would be good for the company as a whole end up scrapped because the individual departments involved cannot agree on how to spread the profits/risks internally. Also a lot of work ends up duplicated because it is 'cheaper' to get someone in your department to do it rather than to 'pay' a rival department to be allowed to use their solution.

Basically you end up losing many of the advantages of scale that a big company should provide without gaining most of the advantages of flexibility and nimbleness that a small company should provide

I'm not sure how you would work out how many tokens a department has to give. My hope is that there would be a way to incentivize going outside your team/department to get help.

OK, so it's not automatically a disaster, but companies have attempted to do this with "virtual org" and clouds of freelancers. It only works for certain types of piecework and small organisations. For larger things it's simply impossible to write the required contracts. This is part of why the London Underground privatisation failed: contract documents were heading into the millions of words and still inadequate to describe the working relationships.