Increasingly that kind of requirement puts you in the same camp as oppressive nation states. Being a network operator and wanting to MitM your DNS makes you a political actor. Devices you paid for, but don't actually own, will end-run your efforts by using their own hard-coded DNS servers. (See https://pc.nanog.org/static/published/meetings/NANOG77/2033/...)
Though I fully understand I'm in the same camp as oppressive nation states. But until my kids get older I'm in charge, I need to set them up for success in life, which is a complex balance of letting them have freedom without allowing them to make too many bad decisions. Not getting their homework done because they are watching videos is on bad decisions I'm trying to prevent.
Not just devices, Jetbrains software has hardcoded DNS too. I've had to resort to blocking its traffic entirely because of the sheer number of servers and ports it tries in order to work around my DNS blocking, now I allow traffic only during license/update checks. I'm sure other large vendors do something similar.
https://intellij-support.jetbrains.com/hc/en-us/community/po...
So really instead of thinking about this like "parents are acting like nation states" I think it's much better to think of it like "parents are countering corporate nation states."
I was thinking more about embedded devices that people buy but don't own (Chromecast devices, "Smart" home doodads, etc). You can stick them in a VLAN and filter their access to the Internet but they're inscrutable inside and have opaque, encrypted communication with their "mother ship".
I think your goal with your kids is laudable. I do the same thing. It limits the ability to use off-the-shelf devices and software, and I'll get more flak about it as my daughter gets older and is excluded from the "social" applications that I can't allow her to use because they're closed-source and not able to be effectively filtered. I'll burn that bridge when I get there, I suppose...
One day they will do both, but that day is probably far away.
And they are on my network, so if they don't function without their own DNS that's OK by me.