So I connected my Osmo Pocket to my iPhone XS Max and viewed my previously recorded videos on the bigger screen. When I tried to select some videos and save them to my phone I got told it’s “not possible on current model”.

Is saving to phone going to possible in a future update?

Thats a known issue at the moment.  There is another thread that talks about this, and mentioned something about its due to the videos being at a 100mbp bitrate, which the "Photos" app on iOS does not support.  Something along those lines anyway.

Hello there, may I verify if you are referring to the footage of 4k, 60fps? Did you try other resolution to see if they can be downloaded to your phone?

I’ve tested on iPhone 7plus, and it applies to any 4K footage, 30 & 60 fps on mine. I can only download 1080 footage currently. Quite frustrating.

Same here..cannot dowload 4k video using my xs max

$31 after using 60% off coupon.
Mine arrives today.

https://forum.dji.com/thread-180246-1-2.html
https://www.amazon.com/gp/product/B06XXY4TP7

I suggest using YouTube2Video. It has worked well for me. It is a free YouTube video to mp4 converter through which you can download unlimited videos to your iPhone not only from YouTube but from other websites as well.