The S should just simply own the E (wholly or partly) but try not to manage it.
Our gov’t should change the way it does business with startups that benefit from our taxes. Many publicly traded companies got their start via grants, subsidies and R&D effort from the gov’t (Google, Tesla, etc…). The gov’t should get something in return for it a la a venture capitalist does. We take a chance on your company and in return you’ll give us x% of shares/ownership of your company.