With current encrypted SNI proposal, your privacy (between you and the superprovider) is /improved/ by talking to a site behind a large aggregating provider. It sucks (since the superprovider still sees everything), but that's how it is.
edit: added clarifications in (parens)
Every iPhone connects to APNS for push notifications and stays connected, and, last I looked at the protocol, the client certificate was linked to the device serial number. That's quite a geoip tracklog dataset, and AFAIK you can't turn it off.
It's to the point now that to keep my city-level location private from Apple, I'm not putting SIMs in any of my iPhones/iPads any longer, and carrying a battery powered VPN travel router (with a SIM uplink in it) for them to talk to. Super annoying that it has to come to this.
This problem is solved in I2P (https://geti2p.net) by adding a few intermediate hops between you and destination. You will know someone is connecting to the network, but you can't find what they're doing.
You can host multiple web sites in the same port since the 1990s, using name-based virtual hosts (https://en.wikipedia.org/wiki/Virtual_hosting#Name-based). It's rare nowadays to use a port other than 80 (for http://) or 443 (for https://) for public web sites.
[1] https://blog.powerdns.com/2019/09/25/centralised-doh-is-bad-...
[2] https://blog.apnic.net/2019/08/23/what-can-you-learn-from-an...
It does have its limitations; a MITM can still just as easily see which IP addresses you connect to and determine which websites are associated with those IPs. But ODoH isn't really meant to fix that. A VPN would be better suited to fix that particular privacy concern.
So I don't know to what extent this protocol can be useful.