Nuno didn't want to play 4 at the back. He was mostly 3 at the back at Wolves. He was forced to because it was right after Levy had that bullshit announcement about Spurs getting their identity back.
The entire point of a DOF is to keep the system at Spurs consistent no matter who the manager is so we don't have to keep buying different players for different managers. I'm not saying Conte doesn't have an influence but it still needs to fit within what Spurs overall plan is (if we even have one).
If we targeted Nuno due to a Paratici vision for 5 at the back and then Levy overruled I'd be surprised .. despite my dislike of him I don't think he's an idiot, and hiring a Director of Football and immediately overruling his vision would be idiotic.
I'm not sure Paratici fits the bill of a DoF who sets a very clear footballing vision, I just don't really see that.