This is "fixed" in DoH the same way it's "fixed" for encrypted SNI: by having a small number of superproviders servicing millions of domains.

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)