That would actually have fit well within the fairytale framework and still had the desired results on Emma. Say, she gets adopted as an infant, since beautiful, healthy baby girl mysteriously found in the woods with no sign of a family is going to have a waiting list to adopt her. She lives with a loving, caring adoptive family until she's about ten (the age her mother was when her mother died, for symmetry), then something happens to her adoptive parents (fire, car wreck, plane crash, etc.). They don't have extended family to take her in, so she lands in the foster system, and a 10-year-old is a lot harder to get adopted than an infant. Having had a good home and then being thrown into foster care would certainly lead to WALLS because it would have been a harsh contrast rather than the only life she ever knew. Then she runs away a few years later to find her birth parents so she'll have a home.
I guess in this scenario Pinocchio would have had to be adopted separately, or he did get adopted with her but got in with the wrong crowd and still ran away when he was young enough that she wouldn't have recognized August? And you've got to wonder what he told the authorities when they were found. Did he claim to be her brother? Did he tell them his name was Pinocchio? He wouldn't have known that he was a character in a story (and Disney movie) in that world, so he'd have had no reason to give a fake name. You've got to wonder what they'd have thought about a kid claiming to be Pinocchio.
I don't know, I kind of got the impression that they meant to show that her giving him up was wrong, especially in later seasons when that was contrasted against Regina The Perfect Mother. There was that rewind when she and Henry were given fake memories of her always having raised him, which made it look like that time around she made the right choice (with no mention of how she managed to pull off looking after a kid. Was she dragging around a small child when she ran into Cleo and got into the bail bonds business?). There was that weird echo of her saying she needed to give Henry his best chance when Cora abandoned Zelena because she needed to give herself her best chance. And there was the way they kept bringing up the effect on Henry of being given up, with her protests about not having really had a choice and doing it to give him his best chance coming across a lot like Neal's "I had no choice" about sending Emma to prison. Then again, the show seems to have really thought Neal had no choice, so that may just be the way I took it.
It did seem like in seasons one and two that they presented it as the only choice Emma really could have made, but then when they started whitewashing Regina and trying to downplay the heroes, it was recast into some kind of selfish or cowardly choice.
Though that goes beyond just having a child. Instead of having a mutual romantic or even sexual relationship, she controls Graham via his heart and forces him to have sex with her. Nottingham was in town, and they'd hit it off in the past, but it doesn't seem like she ever tried to honestly get together with anyone. She just used Graham as a sex toy. So that seems like less an indictment of adoptive parents and more just Regina being Regina, not being able to deal with someone she couldn't control, wanting it all but not being willing to compromise.
Ah, one of my favorite bits of headcanon -- little Hook dumped in a port town the next time the ship where he was abandoned by his father came in to port, fending for himself, then rescued from street toughs by Liam, the son of a prominent admiral, who then adopts Hook. It would have explained his abandoned child backstory plus his fancy education and rapid rise in the navy, plus his hero worship of Liam (and Liam's rapid rise in the navy). Then there was a bit about how the admiral learned what the king was up to and raised objections, so the king sent him on what amounted to a suicide mission, and then the mission Liam and Killian were sent on was also meant as a suicide mission to tie off all the loose ends. That makes more sense than two random guys getting to be officers because they found a gemstone, and they still manage to move up in the navy with minimal training.
Up to a point, it can work pretty well, since parents will do just about anything for their children and that provides a strong motivation, but I think they overused it to the point of cliche, and then they retconned things so it was diluted. That initial revelation that Rumple had rigged the whole curse so he could reach his son made for an interesting twist, but then they showed repeated other means of traveling between worlds, plus his son was in a place he could have reached at any time when the curse was cast, and he had means of knowing exactly where his son was. And then they never got into the complexity of how many lives he destroyed to reach his son and what his son thought of that. I don't think Cora was ever really doing anything for Regina's sake. She was doing it for herself, planning to rule through Regina or through Regina's child (the reason Regina drank the potion to make herself barren). But then that didn't make a lot of sense for Cora's character. She wouldn't have been happy pulling the strings for someone else. A terrible tragedy would have struck all of Henry Sr.'s older siblings and she'd have ended up as queen.
I think that "doing it for the kids" was mostly used to absolve the villains (and as a writing shortcut for a quick and easy motivation). Then they showed that the Charmings were willing to sacrifice their child for the good of their people (but Snow wasn't willing to sacrifice Regina for the good of her people). So I guess the villains were supposed to be better parents?