I'm not sure how firefox could implement this entirely on their end. There would need to be cooperation on the OS (or dhcp client) side to expose that option somehow.
We're in this mess because OSes haven't acted and Mozilla has had to take matters into their own hands. Unfortunately any solution that requires cooperation from other software is going to take a lot longer to land.
I do hope it happens eventually, and I'm sure that when it does Mozilla will change Firefox again to respect that.
It can get even more complicated when you have multiple connections on your machine, each with a different DNS server. You'd need to match the DNS server determination algorithm of the operating system to remain consistent, which is one hell of a task.
There's also the fact that there's no DHCP option reserved for DoH/DoT/DNScrypt (yet) which requires some standardisation work.
There's various APIs to read the current DHCP configuration for a network interface so technically it shouldn't be too hard (at least not when it comes to Windows or macOS where there's standard APIs, as opposed to Linux whose modular layout makes finding a standard location for DHCP config difficult).
If you have multiple connections, each of those DNS servers should return the same answers.
If they do not, they should be marked as forwarders for their respective domains. Something like `Add-DnsClientNrptRule -Namespace "domain.com" -NameServers "1.2.3.4"`
The operating system will have this information; an application, like browser, won't.
I don't think so. Someone like Mozilla can "claim" a DHCP option code and say "this is what we are going to use, operating systems can climb aboard if they want."
We're in this mess because OSes haven't acted and Mozilla has had to take matters into their own hands. Unfortunately any solution that requires cooperation from other software is going to take a lot longer to land.
I do hope it happens eventually, and I'm sure that when it does Mozilla will change Firefox again to respect that.