I also very much doubt it would be a competitor for AdSense.
I have been with Amazon since 1998. An interesting thing was when AdSense first came into being, many very successful Amazon Associates found that AdSense either didn't work for them on their sites or even worse, they sent potential sales away for the price of a click.
As far as I know [I'm open to correction] Native Shopping Ads are just another Amazon innovation for existing Associates. Not for people outside of the Associates programme.
Personally, from disappointing experience I am loathe to embrace Amazon suggestions just as much as I am about AdSense suggestions. So much depends upon your site, your genre, your audience.
There is no such thing as one size fits all.
Looking through the Associates Forum [which I rarely do these days] I see the usual list of complaints/problems relating to Native Shopping Ads.
Amazon Associates Forum: [engagedforums.com
I certainly cannot visualise it remotely being a competitor to AdSense though.