Original text:
9.  Running DNS over HTTPS relies on the security of the underlying HTTP transport.  This mitigates classic amplification attacks for UDP- based DNS.  Implementations utilizing HTTP/2 benefit from the TLS

Reviewer comments:
Is there a reason not to make a recommendation for the case of a DOH-only service? The current text says: Implementations of DoH clients and servers need to consider the benefit and privacy impact of all these features, and their deployment context, when deciding whether or not to enable them. Would you consider a recommendation like "For DOH clients which do not intermingle DOH requests with other HTTP suppression of these headers and other potentially identifying headers is an appropriate data minimization strategy."?
NAME That could be added, but it would need a lot more text because your proposed text only deals with one layer (HTTP) while the text above it also talks about fingerprinting with TLS, TCP, and IP (in reverse order). The WG can decide whether adding recommendations for just one layer is worthwhile or possibly misleading about the overall privacy.
NAME It was only an example, and I would be happy to expand. That said, I think this is the most likely source of leakage: folks using a general purpose HTTP subsystem that carries information not needed for DOH requests. Actually recommending data minimization there, rather than saying "it should be considered" seems like a worthwhile thing to do in my personal opinion.
Agreed with Ted (on the list) that this conversation should be on the list. Locking it here.
I have unlocked the comments so that people can propose specific wording changes as diffs in the PR itself; most questions and suggestions should be done on the list.

Revised text:
9. <ins> RFC7626 discusses DNS Privacy Considerations in both "On the wire" (Section 2.4), and "In the server" (Section 2.5) contexts.  This is also a useful framing for DoH's privacy considerations. 9.1. DoH encrypts DNS traffic and requires authentication of the server. This mitigates both passive surveillance RFC7258 and active attacks that attempt to divert DNS traffic to rogue servers (RFC7626 Section 2.5.1).  DNS over TLS RFC7858 provides similar protections, while direct UDP and TCP based transports are vulnerable to this class of attack. Additionally, the use of the HTTPS default port 443 and the ability to mix DoH traffic with other HTTPS traffic on the same connection can deter unprivileged on-path devices from interfering with DNS operations and make DNS traffic analysis more difficult. 9.2. A DoH implementation is built on IP, TCP, TLS, and HTTP.  Each layer contains one or more common features that can be used to correlate queries to the same identity.  DNS transports will generally carry the same privacy properties of the layers used to implement them. For example, the properties of IP, TCP, and TLS apply to DNS over TLS implementations. The privacy considerations of using the HTTPS layer in DoH are incremental to those of DNS over TLS.  DoH is not known to introduce new concerns beyond those associated with HTTPS. At the IP level, the client address provides obvious correlation information.  This can be mitigated by use of a NAT, proxy, VPN, or simple address rotation over time.  It may be aggravated by use of a DNS server that can correlate real-time addressing information with other personal identifiers, such as when a DNS server and DHCP server are operated by the same entity. TCP-based solutions may seek performance through the use of TCP Fast Open RFC7413.  The cookies used in TCP Fast Open allow servers to correlate TCP sessions together. TLS based implementations often achieve better handshake performance through the use of some form of session resumption mechanism such as session tickets RFC5077.  Session resumption creates trivial mechanisms for a server to correlate TLS connections together. HTTP's feature set can also be used for identification and tracking in a number of different ways.  For example, authentication request header fields explicitly identify profiles in use, and HTTP Cookies are designed as an explicit state tracking mechanism between the client and serving site and often are used as an authentication mechanism. Additionally, the User-Agent and Accept-Language request header fields often convey specific information about the client version or locale.  This facilitates content negotiation and operational work- arounds for implementation bugs.  Request header fields that control caching can expose state information about a subset of the client's history.  Mixing DoH requests with other HTTP requests on the same connection also provides an opportunity for richer data correlation. The DoH protocol design allows applications to fully leverage all the features of the HTTP ecosystem, including features not enumerated here.  Implementations of DoH clients and servers need to consider the benefit and privacy impact of these features, and their deployment context, when deciding whether or not to enable them. Implementations are advised to expose the minimal set of data needed to achieve the desired feature set. Determining whether or not a DoH implementation requires HTTP cookie RFC6265 support is particularly important because HTTP cookies are the primary state tracking mechanism in HTTP.  HTTP Cookies SHOULD NOT be accepted by DOH clients unless they are explicitly required by a use case. 10. </ins> Running DNS over HTTPS relies on the security of the underlying HTTP transport.  This mitigates classic amplification attacks for UDP- based DNS.  Implementations utilizing HTTP/2 benefit from the TLS