The "should not" is an opinion - SAFs - made with the benefit of hindsight. Nothing more.That brings the rather unsettling possible conclusion that Utd knew he was going to make a mistake and just let it happen. Just to restate as SAF stated "Nonetheless, he did go on to say that Moyes should not have disbanded the backroom staff which had been there under Ferguson.
The "should not" doesn't allow for a "it seemed like that might be the right thing to do it but just didn't work out well" analysis but that it was allowed to happen (so not a comment made with the benefit of hindsight) but clear that it should not happen.
It's also worth noting that SAF was acutely aware of the effect Sir Matts continued presence around the club had on his immediate successors. I think SAF made a conscious decision to try and avoid that scenario reoccurring.