I had a lot of use for this for a few years, there was a window where I had my first laptop's hard drive die a horrible death, but I could not afford a replacement.
Enter Knoppix and persisting any state I cared about on a thumb drive.
Of course, since RAM was so limited on devices, just installing packages and leaving the modifications taking up valuable RAM was inconvenient to do, so I went down a rabbit hole of customizing the image builds with various nonsense.
Useful dozens of other times before Ubuntu popularized live images just being a thing you supplied as table stakes, but that window of going down a customization rabbit hole and running a diskless laptop is what I remember.