> the concept of people thinking of their clones as children is wild

I dont think so. The clones would be children in every sense that matters to society. They grow up to be adults, like any other human and with the disclaimer that early experiments will have genetic problems. Cloning is a go-to strategy for situations where traditional/assisted procreation is failing catastrophically or unavailable (eg spacefaring colonies that are sterilized mid-transit).

Treating specific genetic sequences as a legally special class, is a different discussion that arises in treating clones as something other than children, as they are literally descendants.