Why firms stay private longer?

Yes, Sarbanes-Oxley is one well-known reason but there are more reasons, most of all stemming from a shift in the balance of power toward founders, boosting their ability to raise private capital:

One such notable deregulation event has been the National Securities Markets Improvement Act (NSMIA), passed in October 1996. NSMIA has made it easier for both private startups and the private funds investing in them to raise capital. First, NSMIA exempts private firms selling unregistered securities under Rule 506 of Regulation D from state securities regulations known as blue sky laws (Rule 506 is one of the exemptions firms can use to issue private shares not registered with the SEC). As a result, NSMIA has made it easier for startups to raise private capital from out-of-state investors by exempting private firms from complying with the blue sky laws of every new state where they issue securities (public firms have long been exempt from blue sky laws). Second, NSMIA has made it easier for private funds such as venture capital (VC) and private equity (PE) funds to raise large amounts of capital by increasing the number of investors in a fund that force the fund to register under the Investment Company Act (ICA).2Registered funds have to regularly disclose their investment portfolio and face leverage and other restrictions, and so VC and PE funds tend to avoid having to register.

That is from a new NBER working paper by Michael Ewens and Joan Farre-Mensa.