There isn't a surplus of newborns needing adoption; many government agencies get paid based upon the number of children they manage, so they have little incentive to expedite adoptions. Foreign agencies are much more cooperative.
I'm not sure what you mean about "no strings attached" adoption. People need to be screened before they adopt. I don't see a problem with that.
It used to be that once an couple took in a baby and completed the adoption, they could rest assured that anyone else's claims to the child were extinguished by the adoption. There may be some vaguely conceivable exceptions (e.g. if the child in fact turned out to be a kidnap victim), but such possibilities were far too remote to worry about.
Unfortunately, some meathead judges have determined that if a woman who gives away her baby turns her live around and later wants it back, they should give serious consideration to giving her the baby (and in some cases actually do it). Not sure that should make a top-five all-time list of bad judicial decisions, but probably the top twenty or so.) Prospective parents may be loath to adopt children from places where such judges might snatch them back. Foreign adoption avoids that risk.
I see your point. But there have been cases where foreign parents have gotten their children back. There was one not too long ago but I don’t remember the details. It was in the news, though. It is older children that have a very hard time finding families. If you do a search and read some of the stories, they will break your heart. Children just wanting loving families. I think we often take a lot for granted in life, like having loving families. God bless those who adopt.