Move bug workaround for old resolvers past the Private DNS codepath

There's an anecdotal bug where a buggy resolver might drop queries which are sent too close together. We have never observed this bug directly, but we assume that it might exist in very old resolvers. Private DNS resolvers implementing DoH and DoT are modern codebases and thus shouldn't need this workaround.

Change-Id: Id0242063791fd295fa584b7b46e8938a62c71f42