It's dead right that open source provides tremendous value for companies and that open source projects tend to capture only a fraction of the value they create.
This project looks like a much simpler response to the problem: if a handful of companies signup to support the platform then the platform will make it easy for other companies to support the development of the software their businesses rely on.
While sponsors won't have any control over the projects they are funding, they will have access to a Sponsors-only issue tracker on GitFund with support for upvoting issues — thus gently nudging the maintainers on what they consider to be important.
I wonder if this Sponsors-only issue tracker be visible to the public? Although I suppose you could argue this sort of thing currently happens behind closed doors anyway...