Certainly, the visual stimulation videos help in cognitive development and there are plenty of researches on this. Nevertheless, we often try to look so far that we ignore a puddle that's very near!
The visual things (videos, games or the like) help in cognitive development. However, in the question, OP's confused about videos for infants or for kids. As the title reads infants (and that's why I answered that way) and in question body 'kids' cognitive development is mentioned!' Certainly, infants' eyes are more delicate and sensitive as compared to kids. Anyway, Ali asked me about the research and here it is.
I personally believe that babies should be kept away from LED, LCDs or for that sake, any monitor emitting rays. No matter how great claims are made by the manufacturers, babies' eyes are delicate, too delicate and sensitive. I personally would avoid this. Cognitive development over weakened eyes is not any parents would want, do they?
Now about cognitive development -this can happen in number of ways not necessarily in the monitors! There are toys and games available that help them learn better things. The children in ancient days too were witty without any electronic gadget. The cognitive development does come through observation, inherent capability of grasping things and above all, the way the thing is taught or represented.
I DO NOT DENY that such videos are not useful. The method is very useful but the medium is not suitable at that tender age. Let them grow a bit, their sight become stronger and their eyes' development mature enough to catch the rays. And hardly, it'll take a year or two. In addition, at that age too, I'd recommend the monitors to be kept as far as possible. First eyes then intellect! (I have had -5 number glasses since my childhood and I know how poor sight makes our lives).