I've just watched it and this is my take :
Whilst it's true that the women who did this were as one foundling put it "tortured souls" their MH struggle does not trump, nor is it less than the profound life long MH struggle of "my mum not only didn't want to keep me but just dumped me, a helpless newborn, to my fate with no regard for whether I lived or died before I was found"
So in my view the Foundlings are entitled to search for answers and the entitlement to keep a skeleton in the closet is mitigated by the sensitivity with which this was handled.
Unless the family consented the mothers and fathers were not named, and did not appear on camera
I strongly got the impression that Jamie's father would meet him but not on camera and didn't actually have a clue he existed which is huge.
Reuniting with birth families is a nightmare for some people, definitely and I know of someone for whom this was the case.
Increasingly this experience will become the norm as opposed to the exception because adopted children are now close to 0% voluntary surrenders in this country and have usually been removed at birth only if other children were removed before them.
The show still mostly features Unmarried Mums Of The 50s-70s and has yet to tackle the more modern adoptive background
It also glosses over the complexities of bonding with strangers who are relatives who are relative strangers and does try and focus on happy ever afters.