And, like you said, this is a bad idea. Is there something wrong with efforts like DNSCrypt + DNSSec? That's supposed to provide authentication and encryption to DNS without sending everything over HTTP.
Did Mozilla just totally ignore the work that's already been done in this area?
DNSCrypt is a niche protocol that basically does do what DoH does. Very few people use it. You can use it instead of DoH, if you like; just disable DoH in Firefox and set up DNSCrypt with your system resolver.
Every operating system has a system wide way of resolving names to IP addresses, and every application uses it. This new architecture of building custom name resolution into individual applications might be easier for them to build, but it's crap.
Mozilla is doing two things:
1. Bundling DNS with the browser (e.g. ignoring system DNS)
2. Using DNS over HTTPS
Mozilla could still do (1) and then use DNSCrypt + DNSSEC internally. Then, it would actually be used, but they'd be relying on existing technology that actually fits the use-case, rather than DNS-over-HTTPS.
For the record, I don't think you should ignore the system's DNS, either.