Earlier quoted context omitted.
I don't think it's a market failure. The reality that password-gating software installation at the OS level can be done on most desktops but not most phones is the opposite sign of a market failure. Mobile OSes have increasingly stripped down capabilities in recent years precisely because of anti-competitive practices. The reason standard desktops have not evolved even better parental control features is not because…
You're focused on "password gating" for installing apps, but the largest subject here is websites. (also a nit: very few Linux systems are set up with noexec on home directories, I know "portable apps" exist for Windows, and I assume MacOS has similar dynamics) > the absolute level of demand for parental control features has been low until recent years, and even this recent wave of demand is somewhat manufactured. I…
After curated local content, you could get an old desktop (and later a laptop too) and install a Linux distro of your choice on it, something reasonably modern. Put Minecraft on it, and show your child how to start a singleplayer world. Show them how to use the web browser, and add a curated list of sites in the bookmarks. Leave them to figure out the rest on their own. Withhold the sudo and BIOS passwords at the beginning, but give them the passwords when they're ready. I think for the sudo password, it's when they try to host their own Minecraft server for the first time, and BIOS password when they explicitly ask you for it (though these may never happen, depends on the kid, so set your own milestones). Configure the OS and programs as you see fit early on, but don't make changes secretly after they've had the computer for a few months. Block unwanted sites and limit access times with your WiFi router or OS firewall as you see fit. Eventually, they'll figure out how to get around or tear down the barriers you put up, and that's fine, just pretend you don't know or give them a vague hint if they do something too egregious like stealing the neighbor's WiFi. Gradually loosen your control as they get older. And if something breaks, let them watch how you fix it.
Don't give them a phone. Or even if you do, strip it down so that it can only be used for calls, but you can add apps over time. Don't buy them mobile data. Let them buy their own phone and mobile data when they're old enough to earn the money, and that's when your digital supervision ends.
Regarding a solution that "just works": when your child goes out to play, you're the guide that protects them and shows them around town. You know the roads, buildings, people and rules better than they do. There aren't any solutions that "just work" which exempt you from your job as a guide. Well, there are, but that just means someone else is watching your child for you. I think digital parenting is similar in this regard. Parents needs to understand the digital landscape well enough to guide and advise their kids. Solutions which don't strip away parental rights and responsibilities will require some effort to use.