For me, Amazon helps me sort through many options to select the product that _I_ believe I will like best. I am not stupid. If I see an Amazon branded item I will obviously meet its placement with some kind of suspicion. In fact, I will dig a bit harder into the reviews. Do the batteries really last as long as some of the brand name ones? Let me see if it's worth the cheaper price. That sort of thing.
Amazon can be the e-commerce site and sell commodity things. It would be different if it lacked transparency or was trying to hide it's involvement in the private labels.
To your last point, to me, it feels that they try to hide their private labels. Some are named “Amazon XXX” but most are not: Solimo, Presto and countless clothing brands.
I mostly realise that they are Amazon brands when I notice they are strongly pushed by Amazon’s algorithm.
Amazon can be the e-commerce site and sell commodity things. It would be different if it lacked transparency or was trying to hide it's involvement in the private labels.