Regarding: Institutionalize for their schooling
Children who attend government schools and much of what is considered tradition private schools are Institutionalized for their schooling.
From the Webster definition of “institution: “b : an established organization or corporation (as a bank or university) especially of a public character;
From the Webster definition of “institutionalized”: 2) : to put in the care of an institution.
According to your criteria every child under the age of three will be in an institution. I will bet that this is over the edge and beyond the pale even for those that agree with you.