It doesn't work like that. The hourly rate they are charging for your time also goes to support overhead and employees who aren't directly billable.

Indeed a portion of revenue does cover all operating costs, fixed or otherwise. However in a large org those costs are also distributed across all of the profit generating employees. The comparative overhead on a single employee among thousands is small compared to a sole proprietor's burden. Economies of scale kick in above a certain point as bulk purchases from supplies and larger employee pools for things like insurance increase your bargaining power when negotiating those contracts. The same is not true of an individual. But the conceit of that argument is that it's not zero sum, those prices also include a healthy profit margin. And I'd wager the profit margin is higher on a large company than for a sole consultant.

I'm on the opposite side now. I don't work for a software development company. The people who make us money have to support software development. The development department is considered a cost center. That doesn't mean that I should pay them.

For the most part, what you make isn't derived from how much revenue you make your company. It's derived from what the market will bare. Even if you are independent, people who are hiring you are going to try to find the largest spread between what they have to pay for development and the profit they can make based on the development.

On the other hand, what are the real cost of being an independent developer? Health insurance, a computer (that we would probably have anyway) and any development tools. We can usually get away with Fred development software.