I guess that would work. For those with internal NUC drives it is probably possible to use the internal NUC drive (or its NAS backup) as a share mounted over the LAN - won’t be super fast but I guess good enough. If on wifi probably don’t go crazy with hires 
No iPhone experience, but according to this it’s just as easy as on Android:
Then of course you need a router that allows that.
The other option is plugging a USB wifi dongle into the NUC and connecting to the phone as the wifi hotspot. The problem there is that you might be sending quite a few dongles back and forth from Amazon until you find one that works at all and then works well. Described here:
Look for Linux support in the Amazon comments, but this isn’t completely reliable as the Chinese manufacturer may well change the chipset in what looks like the same dongle