> It cannot then inspect further traffic but it certainly can log your IP address and all URL's a given IP ever hit.

Correction: they can log host names/IPs, not URLs. The path of any given URL is part of the HTTP header, invisible to onlookers (assuming HTTP and assuming HTTPS is uncracked).

Considering that the DNS in question is third-party, that is, it's independent from the ISP. Then the DNS and the ISP will not share data with each other on a routine basis, which would make this concern negligible for every day traffic.

So to simplify, the DNS provider has a map of IPs to Domains visited, while the other hand an ISP has a map of IP addresses to identities.

To even cross-reference the data, the ISP and the DNS provider would need to partner, and violate their privacy guarantees.

At the very least it's obvious that using a separate DNS provider than your ISP's provides additional anonimity by decentralizing your traffic. Although this comes with a tradeoff, having 2 providers increases the odds of partial leaks.

This analysis is so overkill for your personal traffic that it borders tinfoil territory, if we are in a professional setting and are discussing the competitive data of a company or that of thousands of users, then this level of scrutiny is merited, but as-is, separating your DNS provider from your ISP is already very marginal and a bit paranoid. Evaluating the DNS providers to such an extent that a huge security company with good legal standing would somehow qualify as unsafe, for the traffic of one user, I stress, is paralyzingly over-engineering the security of an infrastructure that has already been secured such that users don't need to know what a DNS and how to configure it in order to have safe and private internet.

Imagine going to the bank and asking the teller for a withdrawal but not disclosing the amount and coming up with a mechanism to withdraw without anyone from the bank knowing what you withdrew. Sure, it increases your security, but also come on, what are we doing here?

Hi. If your response involves explaining the very very basics of DNS to someone that clearly knows what DNS is, please consider the possibility that you may have misunderstood them instead of lecturing them on the basics of ubiquitous internet technologies.

How could that experiment work?