>But why not Faculty? It has proved successful in its field and is a leading UK AI firm
No, they're not. They're a boutique business intelligence and data strategy consultancy with a specialism in doing small- and mid-scale, non-secure public sector project work. They are not a significant player in the AI industry - they haven't published any significant research, they don't have significant products and they don't push the boundaries of what the industry does. They're well-connected powerpoint jockeys who know a spot of python on the side.
The "leftish media's" issue with them is largely down to the fact they are closely entwined with the web of companies associated with Rob Mercer. While it's true they did not work "directly or indirectly" with Cambridge Analytica, they did just so happen to employ a number of recently ex-CA people at the core of the team who worked with Vote Leave during the campaign. Faculty have since leveraged those political connections to hoover up well over a dozen small, and some more not-so-small, data contracts in the heart of Whitehall. These contract wins have largely been done on a non-competitive basis, further raising eyebrows given Faculty's lack of delivery track record or expertise. Similarly, key Faculty staff managed to worm their way into the heart of the government's coronavirus response, including inexplicably attending SAGE meetings, again despite any kind of competence in scientific advisory, epidemiology, research or incident management.
It should be noted that the "leftish media" in the form of The Guardian are also a significant investor in Faculty, so it's hardly like they're throwing rocks at the enemy.
Given Cummings's well-deserved fall from grace, I would expect Faculty's influence over the public sector to wane in the immediate future.