it's just the good ole' plain moral thing to do (not a great argument, for sure)

On the contrary, I think this is the very strongest argument you could make. What other reason is there to act, except that it is right?

Of course, this argument will not work for people who do not agree with us that Making life easier for struggling new parents is good. I think such misanthropes are rare and I am willing to ignore them.

If your position were "We should make life easier for struggling new parents because it is good" I would march alongside you.

Instead, I read your position as

"We should divert resources, taken from others (including struggling new parents), to give new authority to the body which terrorizes struggling new parents with terrifying goons, to force businesses to alter the voluntary agreements they make with working people, including struggling new parents, such that some workers will benefit and some will be harmed (perhaps by discrimination, perhaps by fewer job opportunities), and we will write a charter for this authority with the words Purpose: To make life easier for struggling new parents because this will make life easier for struggling new parents."

That is a much different position and not one I am sure I can get behind.