Where do you think your DNS resolver gets the answers it gives you? You're just introducing a caching layer between you and whatever external resolver you're using. The first time a machine requests a domain (and every time a TTL expires; look at CDN TTLs sometime) you are effectively talking to the internet just like everyone else.

Do you ever wonder if such activity (basically trying to be invisible) will put you under far more scrutiny than if you were to just 'be normal'? Thinking from the other side of it you would be a high value target to monitor as closely as possible if I were law enforcement. I know it sounds ridiculous but you may actually have more privacy (unless you're actually breaking the law) by hiding in plain sight with the rest of us.

If you talk to an upstream resolver through an encrypted link (both CloudFlare and Google support DNSoverTLS and DNSoverHTTPS, at least) then you at least limit the potential privacy threats.