Why? How websites are ranked "organically" is somethine that is up to the search engine. A user-focused search engine would have no problem including factors like price (for shopping sites) that the user cares about. An even better one might provide the user with options to refine the ranking criteria for each search.

Meanwhile you keep assuming that somehow the site willing to give you the best deal will also be the one winning the advertising bid. That makes no sense as they are also the site spending the most on advertisement which they have to recoup somehow.

> As a consumer, I want to be able to learn about that offer, make my own decision where to buy the pan.

You seem to be under the impression that you would be missing out on an offer without ads. But if you only look at a finite set of links you are always missing some offers - ads only change which offers you see. And they do that not based on any judgment of wheter it would be a good offer for you but only by how much those sites paid.

> What wouldn't show up is lmm-cookware.com, launched early October 2021, who is trying to establish themselves as a new destination for cooking enthusiasts.

If a new site is what users are probably looking for, then it should be top of the organic results. Google and other search engines already use signals like when the site was updated, whether it has a social media "buzz", or what price it's selling something at. It's highly unlikely that spending advertising money is a good signal; yes, promising new companies do spend advertising money, but so do established companies and out-and-out scammers.

Helping the user discover new sites is maybe part of what a search engine should be doing. But mixing ads into the search results is too intrusive and anti-user a way to achieve that (if it even does). Maybe there's a time and a place for advertising, but it should be clearly separated from organic results; Google used to be good at that (indeed they were famous for having advertising that was less intrusive than their competitors), but they've been getting steadily worse.