Privacy benefits would vary with different apps - you'd need to really dig into that.

Any purported benefits might stop mum from checking your browsing history but wouldn't stop a determined attacker, although they would likely need to have things in place to monitor you before you showed up with your USB drive.

I can't really think of what the practical benefits actually might be?

It might feel private, and it might even feel convenient in some cases, but as a general practice it seems like a whole lot of horsing around for very little benefit.