The only argument people make is that you separate your reading from your phoning and it's a weak take that feels like a capitalistic trend to just justify buying more gadgets.
E-readers can go weeks between charges, are easier on your eyes, and - when you're using them instead of your phone - actually help your phone's battery last longer too.
And unless your phone is a "phablet" or a Galaxy Z Fold, that "amazing" screen is probably quite smaller than most e-readers. Which isn't a problem for people with good vision, but for those who need larger fonts to read comfortably, screen size can be a major factor.
There is light coming directly from the book into your eyes when you read a paper book, too.
Since human vision is complicated and I'm not an expert on all the complications, I'm not going to say there are no visual advantages to an e-ink display, but "in a smartphone, the light shines directly at you" is emphatically not a satisfactory technical explanation of why an e-ink display is easier on your eyes.
Also I own an early model of the Kindle Paperwhite, which of course has an e-ink display, and I don't notice any visual advantages.
Also: my Paperwhite's backlight cannot be turned off while the user is using it to read, and it has a "diffuser" to spread the light evenly around the screen just like a backlit LCD display does. I.e., it is shining light directly in my eyes whenever I am using it using exactly the same components that a smartphone with an LCD display does, namely LED lights positioned at the edges of a diffuser. Is the product described by the OP actually different in this regard? I'm not sure, but the OP does discuss the product's backlight.
Sorry if this comment sounds a little angry, but this non-explanatory explanation you've made and that I've quoted has been repeated many times over the years on this site.
I've been using the wrong terminology: I wrote that the Kindle Paperwhite has a backlight. The correct terminology is frontlight.