Does that hypothetical apply when considering the two owners--Jerry Jones and Jeffrey Lurie--had different approaches to football management of their respective teams? Lurie hired and permitted full autonomy over general managership responsibilities to Ray Rhodes (1996-1997), Tom Modrak (1998-2000), Andy Reid (2001-2005), Tom Heckert (2006-2009) and Howie Roseman (2010 to present). The general manager, Lurie inherited when he purchased the franchise in 1994, Harry Gamble, resigned a year later.
Lurie gave himself the title of Chief Executive Officer. The responsibilities of that title, along with those associated with his ownership, seemingly are all that he has ever wanted from the NFL. He has not demonstrated wanting any other responsibilities--like that of being his own general manager--in three decades time.
There is very little to latch a what if onto Lurie doing anything of the sort. He has seemed content on hiring, firing, accepting resignations of multiple, qualified football executives to do the job of his GM. The same cannot be said of Jones.