The poll is about CHILDREN!

The responses so far have been specifically about people's opinions on e-readers and their own experiences with them; the respondents being, I would assume, adults.
However, the poll question specifically asks about children using them - NOT adults - and there is a HUGE difference in both the type of person in question and the type of books - or ebooks - in question, as well.
Most children's books are heavily illustrated - and while I don't have the latest e-reader (I only use the Kindle app on my android, and read an occasional ebook on my PC) I cannot believe that heavily illustrated books of ANY kind can be presented nearly as well or as properly, let me say, as they would in actual physical book form.
I'm no expert, so I cannot say if children of any particular age have the dexterity to use an e-reader "safely" (without dropping or damaging it) but that should be a consideration as well, both for the safety of the device and especially the safety of the child.
Childeren tend to handle books more roughly than teenagers or adults as well - also consider the durability of the e-reader and the possibility of having to repair or replace it if damaged by a child. It would be much easier and cost-effective to replace a children's book should it become damaged or destroyed.
But the first thing that hit me when I saw this question is the illustrations - I have yet to see an e-book that has decently presented illustrations, so my response in that regard would definitely be NO.
And I would like to think that as many generations as possible can have the experience of using actual books - so in that regard as well, I would say NO. An e-reader to them would be just another electronic device - an actual book would be something unique, something that stands apart from anything else in their lives. Something to value, something to enjoy unklike anything else, and something to remember.