I have been teaching children for some time now. I think that it is nearly imposible to expect a child to fully comprehend any martial art he/she studies and take it as serious as would an adult. However, this is no reason to keep them out. In my experience, the children are always looked upon as the future of the art and so alot of effort is put into teaching them.
The most important thing to remember is that they are not adult, so you cannot treat them as you would adult, nor can you hold them to the same expectations as you would an adult.
When I teach kid classes I manage to be stern enough to keep them under control and yet fun and encouraging enough that they, well...they have FUN doing their best. A good balance of these two qualities will make a chidrens class work.
The focus of a childrens class shouldn't be to produce tiny masters. It is to give children coordination, confidence, and a feeling for the basic movements of the art. They may not be that great as kids, but when they start hitting puberty, they will be alot better than someone who started training as an adult.It will be second nature for them. Think about it, how many great baseball players would there be if little league baseball was dismantled because children were not serious enough, and could not comprehend baseball as well as an adult?
Back to the point... I think childrens classes are a good thing and children should be encouraged as much as possible. They are our future.