Seems obvious, but is wrong. If there is a really obvious obstacle to anything, which immediately comes to mind, chances are people addressed this already.
In the US, Firefox by default directs DoH queries to DNS servers that are operated by CloudFlare, meaning that CloudFlare has the ability to see users' queries. Mozilla has a strong Trusted Recursive Resolver (TRR) policy in place that forbids CloudFlare or any other DoH partner from collecting personal identifying information. To mitigate this risk, our partners are contractually bound to adhere to this policy.