regardless of whether the ads are "working" (what does that even mean?), they're additional cognitive load; things my eyes see and add to the overall din that the web has fallen to. I use adblock, but even then, the search results on supposed privacy respecting search engines might be influenced by sponsors for the simple reason that the incentives are not aligned.

The fact that I pay for search or email (proton) is not a proof that the companies are not doing something in secret, but it is somewhat necessary in the trust calculus that I am paying for a specific service to end up getting that service (that is to say, ad free, and not intentionally biased search results).