While individual clients may not be easily identifiable, there's still a measure of identification that could be made, if you were to configure the public key DNS server to send a different (but persistent) public key to each IP address which asks for the DNS record. (Probably an ISP's caching nameserver.)

You can't tell how many people are going to be covered by that public key, but you could probably make educated guesses, or combine this with other metadata.

They run both, or buy data from the company that runs the other half?

I'm not sure I see the point,tbh. If you want to control dns, why not resolve yourself, with whatever cache you need? And if you trust a company to do that for you - assuming the two companies do log "their half" - you're just a data breach, data broker agreement or an acquisition away from a commercial entity having all the data (again)?