While the system is opaque, there's enough data points of people who have gone through it to create a set.
Origin of country matters, so does race. The uniqueness of your job matters as well especially if it "can benefit Singapore society", <S$150k pay not so much. If you integrate yourself into society, have locals who can vouch (this one is not opaque, they ask for character references).
"Benefiting Singapore society" is this catch all term and very opaque/hard to pin down. But I've seen middle managers at colleges not get PR while classroom teachers do. But not all things were equal so it's very hard to tell, but there is/are discussions around it.
Over the years it has gotten increasing harder to obtain PR and thusly citizenship.
> Is there a reason they're reluctant to treat permanent residents the same as citizens for kid stuff?
My naive guess is, yes there is. PR is a merit based system to gain access to the "full thing" you need to be willing to put in the work.
At the core they need to solve the local population's birth rate problem.