I think there are several issues here, and, surprisingly, I don’t think lack of hand-flying/recency is the most prominent.
Most airlines, on somewhere near page one of their OM A, have a clause that states that the captain can deviate as much as they like from SOPs for safety reasons. I don’t know if EK has the same; they may do. If there is a culture that publicly severely punishes any deviation, even if totally safe, then things are being set up for failure.
If the first thing you think about when anything out of the ordinary happens is “will I get called in/retrained/demoted/sacked?”, then the battle has been lost before a shot has been fired. IMO as pilots we are not there for the ordinary, the mundane, the everyday (although we still have to get that right). We are there for the odd occasion when things don’t go according to plan and it’s not something that is much known about or practiced. Then we earn our money using knowledge, experience, CRM and critical thinking skills; if we are in a state of conflict as to what management will think of it, then our survival instincts have been muted and a suboptimal outcome awaits.