What kind of headers get transmitted as part of the DNS query? With DNS, the nice thing is that it is not a chatty protocol, no authentication, no cookies, no user agent. https is exactly the opposite. It would be nice to know that it is not a new backdoor into tracking people.
[edit]: plus isn't Stateless TLS Session Resumption effectively a cookie?
Even without tickets, having TCP sessions means that server operators can link multiple queries to a single device, even if multiple devices share the same external IP.
This gives server operators more data than plain DNS.
The DNSCrypt protocol can use a unique key for every query in order to prevent this. Since it doesn't use sessions, and all queries are independent, there is no latency overhead.
For DoH, dnscrypt-proxy has an option to disable TLS session resumption. But it introduces some overhead every time a reconnection is necessary.
[edit]: plus isn't Stateless TLS Session Resumption effectively a cookie?