Don't let phone manufacturers lock the bootloader on phones. Let the device owner lock it with a password if they decide to. Someone will make a child-friendly OS if there is demand. Tech-savvy parents should be able to install that on their kid's phone and then lock the bootloader.
What about non-tech-savvy parents?
There should be a toggle in the phone's settings to enable/disable app installation with a password, like sudo. This will let parents control what apps get installed/uninstalled on their kid's device.
But what about apps or online services that adults also use?
Apps and online services can add a password-protected toggle in their user account settings that enables child mode. Parents can take their child's phone, enable it, and set the password.
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All it takes is some password-protected toggles. They will work better than every remote verification scheme.
The only problem with this solution is that it does not help certain governments build their global mass surveillence and propaganda apparatus, and tech companies can't collect more of your personal info to sell, and they can't make your devices obsolete whenever they want.