I use my Movi with an iPhone X, shooting in 4K60 or 4K24 mostly. I noticed that when charging while filming in hot weather, the iPhone can easily overheat and turn itself off. This happened regardless of the video app used (Native, Filmic Pro, Movi). Considering this in addition to the issues with the charging cable, I'd say that charging the phone in the Movi while filming might not be such a great idea. Like Tabb said in the Live Series Q&A: Better charge between shots.
I was using an Anker powerbank with USB. I guess with USB-C fast charging it would have been even worse.