Lots of servers out there support DoH
Unfortunately, it offers no privacy. DNS is usually the precursor to a tls connection, and the domain name is sent in cleartext during the tls handshake. So the same people who would hijack your DNS queries are still privy to them if you use DoH (routers, ISPs, governments, etc).
There is encrypted TLS handshaking for hiding the TLS domain name indicator.
And DNSSEC doesn't provide any privacy to the end user. Both mechanisms provide something of value, and ideally they'd both be used together.
DNS seems eminently easy to secure against eavesdropping, given it is just distributed database, and a slowly consistent one at that. Someone just needs to step up to the plate and make a p2p resolver that communicates with a secure protocol, rather than the naive one spelled out in rfc1035. And with DNSSEC you wouldn't even have to worry about trusting/verifying other peers.
[0] The formal definition of someone who can break you, not the common usage that implies "trustworthy".
The purpose of a naming system is to give users a common way to consistently reference specific things. Anyone should be able to mention a name for a thing, and know that any other user will be able to look up that name and resolve it to the same thing.
GNS missed this lesson. Under GNS, every user has their own, slightly different view of naming; a name which one user is able to resolve may not be resolvable for another user, or (even worse) other users might see it resolve to something completely different.
There are many ways of defining how a "decentralized" naming system should work. This is one of them, and I'm sure it sounds cool, but it is not a good idea. Try again.
That's why I blackhole DoH on my network. Don't connect to my wireless if you want DoH privacy.