That's a losing scenario for Google and a winning scenario for Amazon.
Google is primarily a search engine, as a product. Google shooting itself in the foot by not showing the best results, harms their reputation.
People already go directly to Amazon to search for things to buy. That has been a constantly growing trend for 15+ years. If Google's product goes backwards when it comes to delivering results people want, that will drive more people directly to Amazon and accelerate the trend of going straight to their site to search for things to buy and bypassing Google.
Google has likely already maxed out on search usage in the US, including on market share. Meanwhile online retail is still only ~11-12% of all US retail. That online share will double in the next ten years roughly. Amazon will be the size of Walmart, in retail, in another seven or eight years, further massively expanding its actual customer use.
Amazon easily wins that battle with Google. All of the expansion over the next ten years is on Amazon's side. Meanwhile Google has an aging, maxed out product in search, and a maxed out product in Android (annual global smartphone sales growth is near zero).