I have always wondered: don't adopted children provide another natural experiment, on a much larger scale than the (presumably quite rare) cases of identical tw

I have always wondered: don't adopted children provide another natural experiment, on a much larger scale than the (presumably quite rare) cases of identical twins reared apart? You don't even have to hope there was another child of the same parents who wasn't sent for adoption (although that would certainly help) - simply control for socioeconomic status and everything, and see what the "intervention" of moving a child to an upper middle class family changes. Or not?