Some, probably most, "unicorns" aren't really private. They have shares held by "qualified investors", which can include mutual funds. Fidelity and T. Rowe Price funds own sizable chunks of Uber and Space-X. Fidelity Contrafund owns Uber stock, and anybody can buy shares in Fidelity Contrafund. So, in a sense, ownership in the company is already publicly traded. The SEC allows a mutual fund to put up to 15% of its capital in illiquid securities such as Uber. This was intended as an exception to provide capital to small companies, not a way for a company with a $60 billion market cap to avoid disclosure.

That's what concerns the SEC. When a "private" company gets big enough to be a significant part of mutual fund portfolios, should it have to start reporting as a public company?