I have a Hanvon ereader with a first generation Vizplex E-ink display. The device comes with a screensaver, which just loads some pictures after some time. Does this serve a purpose, such as to prevent burn-in, similar to the purpose of screensavers on CRT computer screens?
Technically it isn't a screensaver since the images are static (unless of course the device cycles through images at regular intervals). Either way, e-ink doesn't suffer from burn-in, so it really isn't necessary.
What a screensaver (we'll call it that) does do is show that the device is sleeping, so it will not respond to commands (either via touchscreen or buttons, depending on the device).
As you said, e-ink displays work differently from computer screens, this is not necessary and I think that the only reason to have a screensaver is for aesthetic purposes.
I have a Kobo ereader and when it is sleeping or powered-off it displays the cover of the ebook that I'm currently reading, I think that this is made to mimic the look of an actual paper book.