Yep, they'll disappear just like the single function mp3 player did.
Wait, hang on a minute, mp3 players still seem to be all the rage (OK I know a lot of them show videos now but there are enough that don't).
You will end up with a mix of single and multifunction devices.
Although the single function devices may be no cheaper if they are better at what they do - I could get a phone that has an mp3 player cheaper than a walkman (or iPod) but it wouldn't be better.
So you may end up with a e-ink (or similar tech) reader that is more expensive than a tablet and as long as enough people buy them some companies will continue to make them.
Although if the multifunction device does the job as good or better then the one trick pony is in trouble - The sat nav on my phone is actually better than my sat nav