Indeed. A DoF is a great thing in conjunction with a sympatico manager, but a terrible thing when paired with a poor or belligerent one... In the end, it ultimately always comes down to the players and the manager. As it always has. A good DoF doesn’t win you titles on their own. But a good manager, and/or good players can.
However much smoke is currently being blown up Klopp’s ass, Brendan Rodgers remains the closest any modern Liverpool boss has come to winning the league, and he did so with no DoF at all!... but also not long after Roy Hodgson had gone full David Moyes under a very powerful DoF in Damien Comolli (who, faults aside, still signed the likes of Suárez, Coutinho & Henderson)
It’s a very relative position.
That said... if there’s one person in the entire footballing world that the very notion of a DoF is objectively ill-suited for, it’s absolutely Jose Mourinho. Because nothing says “Classic Mourinho Meltdown” like “Person appointed to tell him who to buy”...
...but we now live in Bizarro World, where Trump is President, Brexit is happening, and Man United fans think a DoF appointment would’ve not just saved Mourinho, but also acted as some all purpose, deck clearing magic spell of sorts, and instantly restored us onto the path of ultimate righteousness....or something.