Is there a reason DHCP can't be extended to provide DOH, too? As long as the OSes of connecting devices support it, I don't see why not.
This could have been DNS over TLS, or any other form of encryption. But it is DNS over HTTPS. This makes sense only for a browser, because they have the https stack already. But if we are talking about libc, it's very different story, there is no Http, let alone HTTPS there.