- Edited
You are right - it would be best to do this at system level. Mac OS supports that via a .mobileconfig config profile - some examples at https://github.com/paulmillr/encrypted-dns
Unfortunately, the system level DoH stuff doesn't play nice with VPN or application firewall apps (https://github.com/paulmillr/encrypted-dns/issues/13) on Mac OS, so for a lot of people, the system level profile won't really work. People who know what DoH is today are likely running Lulu/Little Snitch or similar, as there will be some overlap in those groups.
Both Chrome and Firefox implement their own DNS resolver (with DNS over HTTPS), seemingly because they want to let users configure this by themselves, and give people the option of DoH (or automatically upgrading to DoH where possible), without relying on the underlying system.