This idea of having a 'defensive coach' is interesting.
Firstly, in our case, I find it hard to believe that Paddy is tasked with organising the defence as a discreet job. For one thing, he was on the staff under Glasner when we had a very different, far more defensively coherent, interpretation of the 343 system. If how we defended was up to him then why would it have changed so much from one manager to the next even though the system remains the same on paper?
More to the point, even if a particular coach or assistant is tasked with focusing on defending, he can only do so much if the possession/attacking sides of the game are not up to him. If the players are asked to get forward in a way that places half of them on the 'wrong' side of the ball when we lose it, then your job as a defensive coach is far harder. You are probably working more on high-risk moments and damage-limitation rather than actual coherent, reliable defensive structure.
Plus, most 'managers' are nothing of the sort nowadays. They don't handle contracts, sales, and signings, or set long term direction. They just work with the players they have. In other words, they are a head-coach. I find it hard to believe that the version of 343 we have seen so far is anything other than Sage's take on it. It is certainly his responsibility at least.
Under Glasner we defended in a deep 541 shape. Sarr and Eze/Pino would drop back to defend as part of a bank of 4 midfielders. Mateta would sit in front of the centre mids, so we had all 11 behind the ball with about 25/30 yards between the font player and the defenders. This reduced the distance the centre mids had to cover, and allowed Mitchell and Munoz to defend as fullbacks (i.e. to mark the opposition winger). That in turn allowed the three centre backs to play narrow, close to each other. That leaves far less space (in our half, anyway).
Under Sage the wide players seem to defend more narrow and a bit higher. That helps them press the opposition defence at times, but leaves Mitchell and Khalili exposed. They, perhaps as a result or by design, often defend ten yards further forward than the centre backs. Hence time and again we see either our wing backs scrambling to get back to stop a winger or, even worse, one of our centre backs coming across to the wide area, leaving less defenders and more space in the centre. Critically, it also means all of our defenders are getting moved about at the crucial moments, and are not set in position.
Even if Paddy is the 'defensive' coach, the fundamental structure is so off that his would be a thankless task.