For me it's quite clear that Luke has been adopting this Pep approach of false full back with Key in particular.
This article gives the analysis of the false fullbacks which were introduced by Pep Guardiola. The profit of the false fullbacks in the final third attacking and defensive transition are mainly discussed.
footballbunsekicom.com
It's all about progressing through to the final third, drawing defenders out allowing space between the centre backs to pass to the winger or the marauding false back. Which in theory makes sense.
But that's where the sense ends. Because in this system it requires players to drop back in when the false full back does go on a run. This doesn't happen. But potentially explains why Statty sits so deep as protection. When he doesn't challenge for the ball and simply drops deeper and deeper it then creates a problem.
The other problem then is the choice of false full back in Key. The position is not designed for the player to run into opposition players but sides pretty much play a trap for us to play into. Allow the centre halves to pass or Key to go on a charge and then close down. It works pretty easily for them.