I can imagine that multiple tabs/windows don't share the same address space, so in case of opening the same website on another browser instance, saving to disk would make sure that the cookie is exposed to other running processes as well.

Saving to disk is probably one of the simplest ways of sharing data between processes, but it's far from the only one (e.g. named pipes)

I’m guessing here, but maybe it’s in case of a crash, it can reload them back when you reopen the browser?