TLS 1.3 (2006) was held up for months-to-years by the "unfortunate limitations of some TLS gateways/proxies", and PCI compliance only requires TLS 1.1 as of this year (2018 — 12 years later).

What solution is available that avoids high-latency additional round-trip requests and would be compatible with today's "unfortunate" gateways and proxies?

DNS-over-HTTPS failed for me constantly while traveling, due to captive wifi portals that try to force you into your browser so they can get your Facebook cookie.

DNS-over-HTTPS does not necessarily address the round-trip concerns, as it is simply a transport layer for DNS requests and does not guarantee the browser's ability to coalesce plural DNS requests prior to sending them up for resolution.

So in light of TLS slowness and DoH unfamiliarity to the marketplace, I personally would expect Mark's described limitations to remain applicable for at least another ten years.