You can't be as deeply involved in your kids' lives if you've got 8 of them. There is a reason why every large family has sibling-parents.

Visible elements of pronatalism are largely focused on assigning a particular family role to women and trying to increase the supply of a particular kind of desirable baby (often white, but sometimes focused on IQ selection and other eugenic elements).

I only know one family with >=8 kids (they have 10) and not that well so I can't really comment on them. I know many with 4-6 kids though. It's true that in most cases the women have a traditional family role (not always though, I know one couple where the wife is a very successful cardiologist and the husband is an athletic trainer). Parental involvement is usually higher in these families than among the 2-3 children, 2 professional parent families I know, mostly because one parent is either not working or working in a reduced capacity.

The eugenics part doesn't match my experience at all. I've never seen any evidence that people who are having large families are motivated by that.

I suspect that parental involvement is higher in aggregate but not when it comes to the time dedicated to each child.

Every younger sibling from a large family that I know was in large part raised by their older siblings.

>I associate the concept of pronatalism with also wanting to be involved in your kids' lives

Then don't because it's just wrong. Very few, if any, of the "more babies, bigger families" types have any interest in or concern for the children after they're born. In fact they're usually the ones fighting tooth and nail to prevent any kinds of programs or services that might help the resulting children and families.

For them it's just a pure numbers game/bizarre sexual fetish disguised as a philosophy.

This is not true among the people I personally know with large families.