Yes but EVERY retailer does this. Every single store brand product you see (Costco, Target, Walmart, CVS, Walgreens, etc.) is a result of this. Cheaper products that meet the same demand as brand name vendor goods.
In fact customers are already trained for this. I walk into a store and I immediately price compare against the store brand. So if people doing the same on Amazon, why shouldn't Amazon be allowed to fulfill that? This was a thing in retailers a long time before Amazon started doing it.
If you look around in retail stores today its easy to see how everyone strong arms vendors just the same. For example, ever notice that all of Target's pen section all have a certain color and text printed on the bottom of their packaging indicating the type of pen (Gel, ballpoint, etc)? Target has forced every single vendor (massive companies like Bic, Sharpie, etc.) that sells writing implements in Target to change their packaging, create new SKUs, do different production runs, and handle the logistics of different versions of the same pen. All to be undercut in price by the Target brand pen.