Oh nonononononono! I'm not saying that! God, I'm sure she'll be a great mother! Of course she won't neglect the baby! But now she has to slowly adjust to this new life of hers and wait at least six weeks for her to get back in her peak physical condition again! I'm thinking of her and her health; if it comes naturally? Sure, write some lyrics down, but her main concern all in all should be her and the baby right now, nothing more, especially work.
Anywho, my opinion is motherhood is a huge life alteration, it would take any woman time to emotionally ready themselves for the years about to come (and they don't have long to do it), and despite how clean it looks on paper, there is no pre-planning or organizing with a newborn, they need 24/7 care and that's going to exhaust Utada.