DoH as a protocol has no issues with HOSTS files. The issue is browsers implementing DoH instead of operating systems. If browsers stayed in their lane, and let operating systems implement DoH, compliant with corporate IT design and systems like the HOSTS file, everything would be fine.
Microsoft has already committed to implement DoH in Windows itself. Browsers just need to stop trying to be their own DNS clients.
OSs didn't implement it though. And they never would unless browsers forced it on them. The right approach is for browsers to bring it in and then when the OS supports it, default to the OS version. But right now I don't know of any OS other than I think android that supports it.
Microsoft has already committed to implement DoH in Windows itself. Browsers just need to stop trying to be their own DNS clients.