On the technical standpoint, I fully agree with Giles: let the browser render pages, and OS do the resolution. This pattern of letting the browser do more and more OS tasks is awkward. It have a couple issues, as is a new protocol, not everyone agrees how things were done, Firefox forces it instead of letting the OS decide, things like that. As it is now, it's a mess.
On the other hand, I see governments fuming over DNS-over-HTTPS (DoH), and that alone makes me wonder why. The old "terrorists and pedophiles" label attached to it implies the government is losing access to something they want to have. As DoH uses the same port as HTTPS (443), it's more difficult to identify a DNS request among all HTTPS traffic, and that does not happen with DNS-over-TLS(DoT).
For people in the "Free World," there's nothing much to fear by letting the ISP know the domains you browse, except more spam and directed ads. For people on the Chinese/Russian/Muslim block, a "restricted domain" can lead to trouble. With DoH in place, and Cloudflare proxy for the "restricted domain", anyone can access anything, and the ISP/government only knows you are accessing one of the myriad of domains protected by Cloudflare. Or Akamay.
I would install a dns-proxy that receives plain old DNS queries and forwards them to a trusted DoH/DoT server somewhere else. So the OS would do the resolution, not my programs.