I would argue that this is more a problem with the legal requirements than with the equipment - the law(maker) has expectations you can’t reasonably fulfill.
Doesn’t make your situation any better of course, the law is the law even when it’s impossible
Clear text DNS is the ultimate compromise, a gentleman's agreement if you want, that benefits everyone. We can see just enough to filter what we are required to by law on a best-effort basis, but we never see what you are actually doing thanks to the prevalence of TLS. DoH just broke that agreement.
It's a sad example of how a privacy solution like DoH will eventually result in less privacy, at least in some environments. And I'm not even considering how DoH will be the excuse for totalitarian regimes to up their surveillance antics.
I'm damn sure once I have to do the trusted CA path that someone is going to sell a deep packet inspection solution and present it at some conference where someone in charge will hear about it and then it will be off to the races.
Designing a device to connect to something over the internet even if the network it's connected to behaves strangely isn't random or stupid; it's just in conflict with your goals. Incidentally, last time I ran into a network with legally mandated filtering, I checked whether a google image search for "tits" worked. It did.
Nope, it behaves fine. The owner of the network is serving under age kids. Push too far and its white lists only and block all other IP and I'm sure we'll get deep packet inspection forced on us. Some folks have serious problems with Google Images Search, but you can actually deal with that.
I would also say anyone hard coding DNS into a device is just absolutely unprofessional. Its basically a red flag that any filtering the owner of the network doesn't matter to them.
I'm generally inclined to think an "always use this manually-configured DNS" option is desirable in that situation. Of course, many devices may have a financial incentive (ads) to actively resist the network owner's attempts at filtering.
Filtering is inherently adversarial, and I expect a reasonably sophisticated user on your network could find a way to access some proscribed content. I also expect the users of concern on your network are under five years old and that most of them lack advanced knowledge of networking. Is there an established standard for what qualifies as a reliable-enough filter?
And that along with DoH is contributing to making my life a pain in the butt. How exactly do you folks who avoid our DHCP's DNS expect us to comply with legal filtering requirements? Also, what happens when your hard coded DNS servers are shutdown?