people would have all the children it was biologically feasible to have

I didn't say that. I merely think that the (world average) birthrates would be well above sustainment level. Three children per family on average would be more than enough for a population explosion.

many people don't want children, or want a smaller number for some non-money-related reason

Unfortunately, if we have a future of many generations of biological humanity without significant resource constraints, memetic selection will make sure most people do want many children. This must happen as long as some people want many children and can teach most of their children to want the same.