It would be more accurate if you said that they have made them at some time in the past but don't appear to do so any longer. The page Hippie Guy linked to was dated 2007. I suspect that, given the prices, they were always a niche product.
just bumping this discussion i have one more concern with 'electric ukulele' on wikipedia.
"An electric ukulele is a ukulele which is electrically amplified. If not plugged in, it can still play acoustically."
I disagree with this definition. To me when someone says electric guitar they mean steel string solid body electric guitar
which unplugged is very quiet and not designed for playing acoustically, they don't mean 'an acoustic electric' which is
an acoustic instrument with a piezo or other pick up for plug in to an acoustic amp or PA to boost the volume for performance.
So i don't agree that an 'electric ukulele' is really playable acoustically in that case they should change the info for electric guitar
to match the same for electric uke.
Acoustic electric ukulele in my opinion is not the same thing as an 'electric ukulele' and really should not be mentioned in this article
because their uses, design purpose really are not the same in my opinion. Having owned both acoustic, acoustic-electric and steel string solid body ukes i can say they are all not the same thing. Just as electric guitar, acoustic-electric guitar, and acoustic/classical guitars have their own purposes.
I don't know if anyone agrees or disagrees but it seems people think ukes like the epiphone les paul A/e concert is an 'electric uke' and i think they have the wrong impression of what an electric ukulele really is. I wanted to change the photo on wiki to match that of a real electric ukulele but i can't figure out how. I feel the information is misleading and not helping those who don't know to understand what an electric uke is all about. I tried to improve on the article a few months ago, in the spaces i could figure out how to edit...but there seems to be some grey area in this article. Anyone wanna add their 2 cents?