Are we talking about a gaming-only PlayStationOS for PCs (which would require dual-boot, if you want to use that PC for other tasks) or a full-blown all-purpose OS?
Frankly I don't see Sony able to make a "full" OS with their manpower and experience and keeping it safe and up to date. As much as I like my PS4... even after 2.3 years it is still lacking many popular PS3-features. How long would it take Sony to develop a "full" OS which can compete with Windows, OSX or Linux, which have been developed for decades (new versions weren't developed from ground zero) to reach their actual feature levels and security?