Digging around in the history of adoption, I'm finding some fascinating bits of what our world was like in days gone by.
Here, for example, is something that directly addresses the very issues we talk about here.

This is a much like a form letter that was sent out to families who were applying to adopt an infant, but where the woman was over forty. It's from the 1940s, so those babies who were too young to have older moms are now in their 60s.
We have given your recent letter telling us of your wish to adopt a baby very thoughtful consideration. I realize that it must be very disappointing to you that we cannot consider your application at this time. However, we know from experience how much wiser and more considerate it is to be realistic about our limitations.
We have only a very limited number of children coming to our care and about 500 families who have applied to us. Although we are constantly striving to increase the number of children referred to us so that we may consider a larger number of families, there has been as yet no substantial increase. For this reason it is necessary for us to choose families not only on the basis of their merits as families, but primarily on the individual needs of the particular children we happen to have coming to us.
Since most of our children are the very tiny infants, we feel that for the present we must limit our applications to those families where the mother is under forty year of age. If we are able to increase the number of toddlers or older children coming to us, we will be happy to consider an application like yours. We do not want to raise your hopes falsely and therefore want to explain what the situation is and the reasons why we must limit the number of applications.
We will, however, be glad to note your interest in adoption and should we get a substantial number of older children, we will be glad to get in touch with you and discuss your interest further.
Ouch.