I'm confused.

Counterfeit goods are clearly bad and a problem, but knockoffs that aren't counterfeit seem to be a good thing from an economics perspective, right?

A knockoff that isn't counterfeit isn't deceiving customers -- it is just competing and competition drives benefits to consumers.

There are many knockoff goods that reach comparable quality as the original, luxury good. We shouldn't support the idea of brands for their own sake. Today, many luxury brands are actually degrading in quality as the only thing customers are buying them for is the status signal more than the actual quality.

What is critical is a customer is informed about the trade offs between the goods to make an informed decision.

When I recently was buying camera gear, I bought some of the peak design bags and accessories (which are amazing). I then also bought some knockoff gear that is compatible with their system. Real:https://www.amazon.com/dp/B07F94FQRB $29.95 Knockoff: https://www.amazon.com/dp/B0FYCB594Y $5.01

I knew what I was buying in both cases. I wouldn't trust the knockoff clips to hold my $3K Canon, but I am ok with the knockoff clips to hold an old, light film camera I also brought on the trip. I made an informed decision and my choice also helped contribute to competition between vendors, which is good for the market as a whole and consumers broadly.

If everyone used these chrome extensions, economic theory predicts that prices would rise for consumers and quality of the original brands would degrade through reduced competitive pressure.

What could be more informative for consumers that simply eliminating knockoffs from their search results would be to increase information. Maybe adding a visible indicator of which company is the established or originator of the design and which are knockoffs would be better than simply filtering them out.