First off, Obi-Wan’s dialogue with Luke in A New Hope is already filled with half-truths, but not everything he says is a lie. He’s protecting Luke from the harsh reality of his father’s fall, but there’s still truth in his words. If we change where Anakin was born, it could make Obi-Wan seem even more deceptive, which I think would undermine his role as a mentor.
Eh… I think the dialogue in A New Hope is just barely vague enough that we could weasel our way out of making this dialogue require Anakin to be from Tatooine. The relevant line in the script is “That’s what your uncle told you. He didn’t hold with your father’s ideals. Thought he should have stayed here and not gotten involved.”
So that’s it… that’s the only line that implies Anakin is from Tatooine. It’s implied indirectly, because Obi Wan says “stayed here”, and the current “here” in that scene is the planet Tatooine. But this is inexact enough that we could interpret it as a slight grammatical blunder on Obi Wan’s part. He could have used “here” somewhat incorrectly to mean whatever location Kenobi/Anakin departed from before fighting in the Clone Wars. (Or you could always just do a fan edit that removes the words “stayed here and” so the sentence reads “Thought he should have not gotten involved.” Mostly kidding.)
Anyway, I know that’s really clumsy, but the thing is, as things stand now with the Prequels, Obi Wan’s line here is already like 95% a lie. Anakin and Owen barely had any relationship - they met for a few hours in Episode 2 - and certainly Owen never expressed any opinions about Anakin’s “ideals” or thought he should have stayed “here” at any point. Owen didn’t even know Anakin until after Anakin already left Tatooine and became a Jedi. So the line is already hopelessly broken.
Regardless, I do agree that the original line of dialogue does, as you say, imply that Anakin is from Tatooine. But due to various later retcons, Anakin being from Tatooine was no longer tenable, in my opinion, and keeping Tatooine as his home planet resulted in a worse outcome than simply ignoring the implications of that one word “here” in Obi Wan’s line in A New Hope.
Now, hiding Luke on Tatooine might seem risky at first — after all, it’s the same planet where Anakin was born — but that’s what makes it so clever. Anakin had such a rough time on Tatooine — being a slave, leaving his mother behind, and eventually losing her — that he’d have no desire to go back. The trauma he experienced there creates a psychological barrier, which makes Tatooine the last place he’d want to revisit. In that sense, it’s actually the perfect place to hide Luke because it plays on Anakin’s deepest pain and memories, keeping him away. So, even though the decision of hiding Luke on Tatooine might seem nonsensical at first, it works perfectly if you introduce a trauma that caused Anakin to not want to return to the planet, which is exactly what Attack of the Clones does. Also, you don’t have to forget that, sometimes, the best place to hide something is in plain sight.
I mean, I’ve heard this before. Vader wouldn’t want to go back to Tatooine because childhood trauma or whatever. I mean… that’s really just pure speculation. You don’t know that. You could guess this would be the case, but it’s also possible Vader doesn’t give a shit. He didn’t seem to care when the Tantive IV showed up on Tatooine at any rate.
Regardless, even if this is true, why would anyone risk it? There’s probably at least a million other remote locations similar to Tatooine. Granted, Kenobi knew some people on Tatooine, so that factored in I guess. But relying on Vader’s continuing trauma to keep him away from Tatooine is a huge risk. I sure hope Vader doesn’t have a therapist.