I agree that that the criteria you gave is probably more relevant for the issue at hand, sure.

And, while definitions may not be super important (as you say), and while it is often fine to redefine a word within some context, I do think the definition I gave is probably closer to how people usually use the word “advertisement”.

My inclination is to stick on an adjective though, and refer to, say, “unwanted ads”, rather than say that the ads in a classified section “aren’t ads”.