I think it depends on the hierarchy. Obviously the longer tenured and more established the coach is would go along way into determining how much input they have. Look at a coach like Bennett, there’s no way any recruitment manager would be able to override his decision, likewise Bellamy, Ricky Stuart, Robinson, Cleary, etc.
The Ponga and Taumalolo decisions upon reflection might seem like misguided decisions but you have to remember the position the cowboys were in at the time, they had won the comp in 2015, prelim final in 2016 and grand final in 2017 with a very established nucleus of players, also Taumalolo was given a 10 year contract off the back of winning the Dally M and being undisputedly the best forward in the game, the 10 year deal was a long term sacrifice to retain him within what the thought was a premiership window