The premise of a paid search engine is such that information still remains free on the web, it is the access to the convenience of a (superior/premium) search product that you are paying for. This is different to what you are claiming?
I'd also go as far to say that paid search is the only model that removes perverse incentives that ad-driven business models for search engines have historically produced. We all know that both Larry and Sergey agreed that advertising in search engines is a bad thing in their seminal 1997 paper, yet we also know how that ended ( no ads -> contextual ads -> privacy intrusive ads -> ?). The pressure from the true customer filling the pockets (advertisers), makes this path hard to avoid given enough time.
A paid search product would face pressure from a very different angle - improve quality of the search product itself or risk losing a customer. This is IMO a much better position to be in from a product standpoint as at least the incentives of both the company and the user/customer are aligned. Business wise, probably less lucrative because of "search has to be free" intertia.
Unlike the Google founders who started off not wanting to do ads, but then relented under financial pressures, we have never been anti-ads. Ads convey information, they can even entertain. They can be a useful economic signal for a buyer and a way for upstarts and smaller brands to get attention and compete.