Where can I find such design specification? All I can find is https://w3ctag.github.io/private-mode/ and https://www.w3.org/2001/tag/doc/private-browsing-modes/ that tell nothing about the short duration of a private session. Some emphasis is put on the necessity that private mode and normal mode should be transparent to the user (i.e. not breaking any normal feature). It should be not possible to tell the two modes apart. If you break a feature like ServiceWorker you are providing a way to detect a private browsing session, and that is a bad thing, worse than anything a SW could provide, in my opinion.