Unless I understand incorrectly, this doesn't seem to make the problem any worse. You'd just have to block the proxy rather than the DNS server. Like DoH, only a problem if that's also the web server.
In order for this to be true the device manufacturer would have to send both DNS and web requests through the proxy. They'd also have to "obliviously" encrypt web traffic as well. Otherwise, a MITM could determine which are DoH requests or determine which server is the proxy server and which are web requests.
This means that the DNS response for the web server would always be the proxy itself, or some set of proxies (and it would have to be the same IP for both wanted and unwanted traffic). What does DNS even add at that point? You'd be better off just making your "wanted" and "unwanted" servers the same server.
