Amazon and e-commerce, in general, have a different usecase for search engines. IME, the two products were people searching for the best solution to a problem and had fairly strong organic channels because they solved the problems people were looking to solve and were blogged about all over the internet.

E-commerce: people are looking for the best deal. You pay google to “show up first” and capitalize on brand awareness once they see your competitors. The customer is going to think, “ah nice, at least it’s on Amazon in case all these other stores are too sketchy.” The other stores probably play a better SEO game than Amazon because /they have to to survive/ while Amazon merely throws money at the problem to capitalize on the brand.

With a ban on advertising the biggest companies the ones we all know will benefit as no alternatives would be known. Some brands can spend endless amounts of money and I wouldn't purchase their product because of past experience or reputation.

Banning advertising would collapse industries or reduce market size and limit any expansion efforts.