There are many problems with that idea.
There's the ones who turn out to be innocent.
It's rarely the case in Western jurisdictions that a judge can order an execution and its done. I think I saw somewhere that in the USA, depending on how old a prisoner is and how long they live, it costs more to keep someone in prison and pay for all the legal procedures required before an execution takes place than just handing out a life sentence.
How many children does a defendant have to abuse before the death sentence kicks in? If it's one, and there's no physical harm or murder, then how do you compare the mental damage done to one child by abuse against that done to children of other murder victims. Or victims of rape, assault, bullying, burglary ect?
What causes the outrage in cases of non violent child abuse when the most likely affect is trauma rather than injury, where its largely absent if that trauma is caused by any other crime. There's no doubting the seriousness of this crime and he needs to be imprisoned to keep him away from further offending. As for the money. Justice costs.