I am the kind of person who is fascinated by family history as it is. I would search out of a need for information, not a need for more parents. If friendship can result, fine. If not, that's OK, too. As a future adoptive parent, I would support my child's desire to search.
Adoption is as ancient as human families.
The process of secret adoption and sealed records is actually a fairly recent development along with the rise of social service and welfare systems in the last century. Blended and adoptive families are not new. However, they used to be created more by death than by divorce. Margaret Fuller and her siblings were wards of an uncle after their father's death, and one brother was adopted by a family known to the uncle. Orphans were often placed as indentured servants or farmed out as laborers.