It does not improve privacy, it just puts all your DNS history in the hands of one provider. Not only that it adds latency for no real gain. HTTP is a terrible protocol for anything time sensitive. (its a fairly bad protocol for anything fast or efficient full stop.)
The better way to do this is encourage/provide DNSsec (so we know that a provider is who they say they are) and then encrypt dns queries between servers.
Firstly that stops everything being centralised by default, (kinda, DNSSec has a chain of trust, so thats centralised) DNS is a massively scalable fault tolerant, distributed key value store. Far faster and more reliable than toys like Etcd and the like.
secondly you don't then loose geolocation/provider steering for nearest/fastest node. (yes you can get meta data from IP, but that's not really that useful, that means the _service_ has to figure out how to route your request, not the upstream DNS.)
But it needs improvements to make its more anonymous, slapping a fast SSL like tunnel on a resolver combined with DNSsec seems like a much better way to do this and dns over HTTP.