Magic binding and obliviating of magical kids. I hate that trope. It's utterly anti-canonical, counter-logical, and were the Ministry of Magic to practice it, so self-evidently counterproductive they'd never dare try it.
If the Ministry obliviated little kids, then where did the Squibs come from? Every squib would be brainwiped by default for failing to get into Hogwarts at all. Yet Squibs are apparently scattered hither thither and yon-- and are fully aware of the Magical world.
And even with obliviation, that just goes back to square one, with a magical child or teenager or adult performing more and more accidental magic, only having no explanation for it and imperiling the Secrecy Act in their panic.
Because no, they can't 'bind' someone's magic in Harry Potter. How do I know? Simple: if they COULD bind magic, they WOULD. Every prisoner in Azkaban would have been bound in that way, even if only temporarily. Yet they are explicitly not! Hell, they didn't even do that to Hagrid, and they had every reason to. They broke Hagrid's wand, legally banned him from using magic, yet never bound it-- and we know it because he practices it with the broken pieces of his wand hidden in his little pink umbrella.
Never you mind the backlash if they tried obliviating and binding wizards. The outcry, even from the Purebloods who feared such measures, would be deafening. And the rebellion against that law would be endemic.
You'd eventually have someone who slipped the noose. A bungled Obliviate, or rebellious friends and relatives would go behind the Ministry's back with a Pensieve to restore their loved one's lost memories...
Best case you'd have the start of a magical society rebellion, an underground of de-obliviated and Unbound wizards. Worst case, You'd have a new Dark Lord. Someone who remembered the magical world, that they had been outcast and their magic bound by those who claimed to be their own kind... They would have every reason in the world to go Dark, go on a shopping spree in Knockturn Alley and then go on a Roaring Rampage of Revenge against the Wizarding World. Maybe even de-obliviating and/or unbinding other outcast wizards, witches and squibs to swell the ranks... if the Ministry thought that the DEATH EATERS were bad, imagine how much worse and more ruthless a band of vengeful dark wizards who didn't want to rule the wizarding world but smash it to rubble.
Especially if they were so pissed they took the easiest route to revenge--- and busted the Secrecy Act wide open. One live show-and-tell at, say, the World Cup...