To illustrate your own book

I was curious to see if most children's books authors illustrate their own books ... and was surprised to find several sources that said that Literary Agents prefer to receive manuscripts without illustrations and if they decided to move forward with your project, then they will hire an illustrator.

I'm just curious if this has been the experience of other Author/Illustrators too?

I used to be able to draw pretty well, but then I broke three bones in my right wrist, and I'm right handed, and now I can't get enough rotation on my wrist to draw very well. Any suggestions on that front either?

I love Dr. Seuss and his illustration style, as well as Mark Kistler of Imagination Station, and I really want to be able to draw again and illustrate my own stories. Besides lots of practice, any tips?

Thank you most Hartly,
J.J. Harlty