Variable ND will act as polarizer since it is made of 2x polarizers. This means that you will have a varying pola effect (depending on angles, etc) ALL the time. This is sometimes a plus (most nature shots) and often liability (people shots).
You decide if this is worth the convenience.
Image quality is crap.
The iphone thing is obviously a publicity stunt... "Maximum mobility" my ass. Could have had both mobility and decent image quality with any mirrorless. dslr, pocket cam, whatever.
Sounds to me that a light body, zoom lens and optical image stabilization is what you need.
The most likely reason is that Premiere recognizes the AVCHD file as legal range and stretches the data to fill the full range, but it likely doesn't recognize the range of the XAVC-S file and imports it as is.
I am not familiar with Premiere but you can use an application that allows to explicitly state the range of the video (for example, Resolve Lite) and repeat the test.
Free video conversion tools on Windows:
any other ffmpeg front-end UI