For Origin Private File Systems, I would not expect any user agent to map things to the actual file system: there are notable functional problems especially on Windows, and it’s a very significant security hazard, all of which is neatly avoided by putting it all in the likes of a SQLite database.
First, the functional problems: file names are going to be a bit of a bother, to the point where if you back it by the actual file system you will require some kind of escaping mechanism, which loses you the exact one-to-one correspondence. Names are sequences of 16-bit code units, which means they need not be valid Unicode (ugh, I wish new additions to the browser platform would just start rejecting malformed Unicode), which will cause trouble on some platforms and will probably not be looked on favourably on others as having the potential to cause trouble in software not written to cope with that (e.g. on Windows I don’t think I’ve ever encountered a name with an unpaired surrogate, though it’s legal; on Linux, paths that aren’t UTF-8 are decidedly more common, though they still have a habit of breaking things). It also allows various file names that are forbidden in Windows at large, though in almost all cases you could with difficulty work around that on a per-process basis by throwing it into POSIX mode and/or using fully qualified (\\.\ or \\?\) paths.
Second, the security hazard: putting files with arbitrary names and contents on the file system is dangerous for a few reasons. The simplest is that there’s various buggy software that automatically reads files that get added to the file system, and more than a few times such software has had bugs in parsers that have led to privileged arbitrary code execution. A key purpose of Origin Private File Systems is that you don’t need to prompt the user for permission, because it’s supposed to be safe. I have no idea if this sort of vector was ever used back in the days when IE persisted its internet cache directly to files on the disk, but I can easily imagine such a thing happening now, and it could be really bad, given the right bug.