I'd mostly blame Southgate.
Even in the last game when the midfield sort of worked, Rice was still being used in a more negative, limited way than he is at West Ham. So it's no surprise that when the same midfield set-up isn't working, he also looks more negative and limited.
Which isn't to say he'd be playing like Pirlo otherwise, he's still a defence-first DM and will look too passive on his bad days.
But Southgate (according to himself) thinks playing Rice and Phillips together "lets" England play with four attackers, as if that's a luxury only afforded by playing two defensive midfielders. It's a terribly negative mindset to apply against a team like Scotland.