The protocol we fondly know as DoH, DNS-over-HTTPS, is now officially RFC 8484 with the official title "DNS Queries over HTTPS (DoH)". It documents the protocol that is already in production and used by several client-side implementations, including Firefox, Chrome and curl. Put simply, DoH sends a regular RFC 1035 DNS packet over HTTPS instead of over plain UDP.
I'm happy to have contributed my little bits to this standard effort and I'm credited in the Acknowledgements section. I've also implemented DoH client-side several times now.
Firefox has done studies and tests in cooperation with a CDN provider (which has sometimes made people conflate Firefox's DoH support with those studies and that operator). These studies have shown and proven that DoH is a working way for many users to do secure name resolves at a reasonable penalty cost. At least when using a fallback to the native resolver for the tricky situations. In general DoH resolves are slower than the native ones but in the tail end, the absolutely slowest name resolves got a lot better with the DoH option.
To me, DoH is partly necessary because the "DNS world" has failed to ship and deploy secure and safe name lookups to the masses and this is the one way applications "one layer up" can still secure our users.