Is it a good practise to involve a child in a statement of purpose to say how my point of view has changed since the birth?
No, the statement is about your motivation in doing research and about your research goals, not about your private life goals.
Having a child is undoubtedly a joyful event which can definitely change your perspective on work-life balance, but now that it's changed, simply state what your current research goals and motivations are.
In the US, doing so may imperil your candidacy in at least two ways:
- Some academics will assume right away that since your children are so important to you that they appear in your statement of purpose, they will automatically take precedence over your degree-related responsibilities. (This is not a hazard specific to academe, but neither is academe free of it.) Academe is a greedy pursuit; it does not typically favor those with competing priorities.
- Some academics, especially those conditioned to industry, will be made uncomfortable by including children a statement of purpose, possibly considering it unprofessional. Children are typically don't-ask-don't-tell in the US; asking is sometimes legally dubious (as it may open a workplace to charges of unequal-opportunity hiring), so telling is unwelcome.
I would strongly recommend against this. Record the epiphany if you like; bypass its source.
The other two answers (as I write this) are useful and (so far as I know, in U.S.) are accurate about facts.
Further, I'd argue against including your epiphany, in part because it is possible to argue that it ought not to have been such a great epiphany, since, after all, many people do work + have families (without playing any gender-biased or other-biased games about whose responsibility the kids are...) That is, even if you don't mean it that way, there is also a large possibility of interpreting remarks about this as though you'd surprised yourself that you were able to do work and have kids, etc, ... Indeed, most of us probably are! But it is a common state...
So, as with other life-epiphanies, I think it does not need to be aired publicly. Even if it doesn't harm your applications, I'd think that it'd make you appear naive about adult responsibilities...